1.
図書
Heinz H. Bauschke, Regina S. Burachik, D. Russell Luke, editors
出版情報:
Cham : Springer, c2019 xix, 489 p. ; 25 cm
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2.
図書
Jim Agler, John Edward McCarthy, Nicholas Young
3.
図書
Hellmut Baumgärtel, Manfred Wollenberg
4.
図書
Sterling K. Berberian
5.
図書
Martin Schechter
出版情報:
New York : North Holland, c1981 xx, 324 p. ; 24 cm
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Preface
Acknowledgments
A Message to the Reader
List of Symbols
One-Dimensional Motion / Chapter 1.：
Position / 1.1.：
Mathematical Expectation / 1.2.：
Momentum / 1.3.：
Energy / 1.4.：
Observables / 1.5.：
Operators / 1.6.：
Functions of Observables / 1.7.：
Self-Adjoint Operators / 1.8.：
Hilbert Space / 1.9.：
The Spectral Theorem / 1.10.：
Exercises
The Spectrum / Chapter 2.：
The Resolvent / 2.1.：
Finding the Spectrum / 2.2.：
The Position Operator / 2.3.：
The Momentum Operator / 2.4.：
The Energy Operator / 2.5.：
The Potential / 2.6.：
A Class of Functions / 2.7.：
The Spectrum of H / 2.8.：
The Essential Spectrum / Chapter 3.：
An Example / 3.1.：
A Calculation / 3.2.：
Finding the Eigenvalues / 3.3.：
The Domain of H / 3.4.：
Back to Hilbert Space / 3.5.：
Compact Operators / 3.6.：
Relative Compactness / 3.7.：
Proof of Theorem 3.7.5 / 3.8.：
The Negative Eigenvalues / Chapter 4.：
The Possibilities / 4.1.：
Forms Extensions / 4.2.：
The Remaining Proofs / 4.3.：
Negative Eigenvalues / 4.4.：
Existence of Bound States / 4.5.：
Existence of Infinitely Many Bound States / 4.6.：
Existence of Only a Finite Number of Bound States / 4.7.：
Another Criterion / 4.8.：
Estimating the Spectrum / Chapter 5.：
Introduction / 5.1.：
Some Crucial Lemmas / 5.2.：
A Lower Bound for the Spectrum / 5.3.：
Lower Bounds for the Essential Spectrum / 5.4.：
An Inequality / 5.5.：
Bilinear Forms / 5.6.：
Intervals Containing the Essential Spectrum / 5.7.：
Coincidence of the Essential Spectrum with an Interval / 5.8.：
The Harmonic Oscillator / 5.9.：
The Morse Potential / 5.10.：
Scattering Theory / Chapter 6.：
Time Dependence / 6.1.：
Scattering States / 6.2.：
Properties of the Wave Operators / 6.3.：
The Domains of the Wave Operators / 6.4.：
Local Singularities / 6.5.：
Long-Range Potentials / Chapter 7.：
The Coulomb Potential / 7.1.：
Some Examples / 7.2.：
The Estimates / 7.3.：
The Derivatives of V(x) / 7.4.：
The Relationship Between X[subscript t] and V(x) / 7.5.：
An Identity / 7.6.：
The Reduction / 7.7.：
Mollifiers / 7.8.：
Time-Independent Theory / Chapter 8.：
The Resolvent Method / 8.1.：
The Theory / 8.2.：
A Simple Criterion / 8.3.：
The Application / 8.4.：
Completeness / Chapter 9.：
Definition / 9.1.：
The Abstract Theory / 9.2.：
Some Identities / 9.3.：
Another Form / 9.4.：
The Unperturbed Resolvent Operator / 9.5.：
The Perturbed Operator / 9.6.：
Analytic Dependence / 9.7.：
Projections / 9.9.：
An Analytic Function Theorem / 9.10.：
The Combined Results / 9.11.：
Absolute Continuity / 9.12.：
The Intertwining Relations / 9.13.：
Strong Completeness / 9.14.：
The More Difficult Problem / 10.1.：
The Technique / 10.2.：
Verification for the Hamiltonian / 10.4.：
An Extension / 10.5.：
The Principle of Limiting Absorption / 10.6.：
Oscillating Potentials / Chapter 11.：
A Surprise / 11.1.：
The Hamiltonian / 11.2.：
A Variation / 11.3.：
Examples / 11.5.：
Eigenfunction Expansions / Chapter 12.：
The Usefulness / 12.1.：
The Problem / 12.2.：
Operators on L[superscript p] / 12.3.：
Weighted L[superscript p]-Spaces / 12.4.：
Extended Resolvents / 12.5.：
The Formulas / 12.6.：
Some Consequences / 12.7.：
Summary / 12.8.：
Restricted Particles / Chapter 13.：
A Particle Between Walls / 13.1.：
The Energy Levels / 13.2.：
Compact Resolvents / 13.3.：
One Opaque Wall / 13.4.：
Scattering on a Half-Line / 13.5.：
The Spectral Resolution for the Free Particle on a Half-Line / 13.6.：
Hard-Core Potentials / Chapter 14.：
Local Absorption / 14.1.：
The Modified Hamiltonian / 14.2.：
The Resolvent Operator for H[subscript 1] / 14.3.：
The Wave Operators W[subscript plus or minus] (H[subscript 1] H[subscript 0]) / 14.4.：
Propagation / 14.5.：
Proof of Theorem 14.5.1 / 14.6.：
Completeness of the Wave Operators W[subscript plus or minus], (H[subscript 1] H[subscript 0]) / 14.7.：
The Wave Operators W[subscript plus or minus] (H, H[subscript 1]) / 14.8.：
A Regularity Theorem / 14.9.：
A Family of Spaces / 14.10.：
The Invariance Principle / Chapter 15.：
A Simple Result / 15.1.：
Trace Class Operators / 15.3.：
The Abstract Theorem / 16.1.：
Hilbert--Schmidt Operators / 16.2.：
The Fourier Transform / 16.4.：
Exercises A
Exercises B / Appendix B.：
Holder's Inequality and Banach Space / Appendix C.：
Bibliography
Index
Preface
Acknowledgments
A Message to the Reader
6.
図書
Colin Bennett, Robert Sharpley
目次情報:
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Banach Function Spaces
Rearrangement-Invariant Banach Function Spaces
Interpolation of Operators on Rearrangement-Invariant Spaces
The Classical Interpolation Theorems
The K-Method
Each chapter includes references
Index
Banach Function Spaces
Rearrangement-Invariant Banach Function Spaces
Interpolation of Operators on Rearrangement-Invariant Spaces
7.
図書
edited by I. Gohberg
8.
図書
Israel Gohberg, Seymour Goldberg ; edited by I. Gohberg
出版情報:
Boston ; Basel : Birkhäuser, 1981 xiii, 285 p. ; 24 cm
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Introduction
Hilbert Spaces / I：
Bounded Linear Operators on Hilbert Spaces / II：
Spectral Theory of Compact Self Adjoint Operators / III：
Spectral Theory of Integral Operators / IV：
Oscillations of an Elastic String / V：
Operational Calculus with Applications / VI：
Solving Linear Equations by Iterative Methods / VII：
Further Developments of the Spectral Theorem / VIII：
Banach Spaces / IX：
Linear Operators on a Banach Space / X：
Compact Operators on a Banach Space / XI：
Non-Linear Operators / XII：
Appendix 1. Countable Sets and Separable Hilbert Spaces
Appendix 2. Lebesgue Integration and LP Spaces
Appendix 3. Proof of the Hahn-Banach Theorem
Appendix 4. Proof of the Closed Graph Theorem
Suggested Reading
References
Index
Introduction
Hilbert Spaces / I：
Bounded Linear Operators on Hilbert Spaces / II：
9.
図書
Ioannis Antoniou and Günter Lumer (editors)
10.
図書
by Vitalii G. Kurbatov
11.
図書
I. Gohberg [and] Yu. Lyubich, editors
12.
図書
edited by Sheldon Axler, John E. McCarthy, Donald Sarason
13.
図書
Ronald G. Douglas
14.
図書
Ivor J. Maddox
15.
図書
edited by I. Gohberg
16.
図書
Adriaan C. Zaanen
出版情報:
Berlin : Springer, c1997 xi, 312 p. ; 24 cm
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17.
図書
par Béla Sz.-Nagy et Ciprian Foiaş
出版情報:
Budapest : Akadémiai Kiadó, c1967 xi, 373 p. ; 24 cm
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18.
図書
Jörg Eschmeier, Mihai Putinar
19.
図書
Vladimir A. Marchenko ; translated from the Russian by A. Iacob
20.
図書
Albrecht Pietsch
21.
図書
Pierre H. Bérard ; with an appendix by G. Besson
22.
図書
Ola Bratteli
23.
図書
Shôichirô Sakai
目次情報:
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Preface
Preliminaries / 1：
Bounded derivations / 2：
Unbounded derivations / 3：
C-dynamical systems / 4：
Index
Preface
Preliminaries / 1：
Bounded derivations / 2：
24.
図書
edited by I. Gohberg
25.
図書
Y.A. Abramovich, E.L. Arenson, and A.K. Kitover
26.
図書
V.A. Sadovnichiĭ ; translated from Russian by Roger Cooke
27.
図書
O.L. De Lange and R.E. Raab
出版情報:
Oxford [England] : Clarendon Press , New York : Oxford University Press, 1991 xi, 377 p. ; 24 cm
シリーズ名:
Oxford science publications
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The Mathematical Formalism of Quantum Mechanics / 1：
The Harmonic Oscillator / 2：
Other One-Dimensional Systems / 3：
Angular Momentum / 4：
Spherically Symmetric Potentials / 5：
Applications / 6：
Factorizations with Applications to the Momentum Representation / 7：
The Isotropic Harmonic Oscillator in an Angular Momentum Basis / 8：
The Coulomb Problem in an Angular Momentum Basis / 9：
The Coulomb Problem in the Basis / 10：
Relativistic Quantum Mechanics / 11：
Relativistic Spherically Symmetric Problems / 12：
The Mathematical Formalism of Quantum Mechanics / 1：
The Harmonic Oscillator / 2：
Other One-Dimensional Systems / 3：
28.
図書
by John Avery
出版情報:
New York : McGraw-Hill, c1976 xii, 221 p. ; 25 cm
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29.
図書
Cora Sadosky
30.
図書
A.S. Mishchenko, V.E. Shatalov, B.Yu. Sternin ; translated from the Russian by Dana Nance
31.
図書
volume editors, L. de Branges, I. Gohberg, J. Rovnyak
32.
図書
Bernd Carl, Irmtraud Stephani
目次情報:
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Entropy quantities / 1：
Approximation quantities / 2：
Inequalities of Bernstein-Jackson type / 3：
Inequalities of Berstein-Jackson type
A refined Riesz theory / 4：
Operators with values in C(X) / 5：
Operator theoretical methods in the local theory of Banach spaces / 6：
Entropy quantities / 1：
Approximation quantities / 2：
Inequalities of Bernstein-Jackson type / 3：
33.
図書
J.B. Conway & B.B. Morrel, [editors]
34.
図書
Kehe Zhu
35.
図書
Bernard Beauzamy
出版情報:
Amsterdam ; Tokyo : North-Holland , New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988 xiv, 358 p. ; 23 cm
シリーズ名:
North-Holland mathematical library ; v. 42
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36.
図書
A.H. Zemanian
37.
図書
V. Hutson and J. S. Pym
目次情報:
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Preface
Acknowledgements
Banach Spaces / 1：
Introduction / 1.1：
Vector Spaces / 1.2：
Normed Vector Spaces / 1.3：
Hilbert Space Problems / 1.4：
Lebesgue Integration and the Lp Spaces / 2：
The Measure of a Set / 2.1：
Measurable Functions / 2.3：
Integration / 2.4：
The Lp Spaces / 2.5：
Applications Problems / 2.6：
Foundations of Linear Operator Theory / 3：
The Basic Terminology of Operator Theory / 3.1：
Some Algebraic Properties of Linear Operators / 3.3：
Continuity and Boundedness / 3.4：
Some Fundamental Properties of Bounded Operators / 3.5：
First Results on the Solution of the Equation Lf=g / 3.6：
Introduction to Spectral Theory / 3.7：
Closed Operators and Differential Equations Problems / 3.8：
Introduction to Nonlinear Operators / 4：
Preliminaries / 4.1：
The Contraction Mapping Principle / 4.3：
The Frechet Derivative / 4.4：
Newton's Method for Nonlinear Operators Problems / 4.5：
Compact Sets in Banach Spaces / 5：
Definitions / 5.1：
Some Consequences of Compactness / 5.3：
Some Important Compact Sets of Functions Problems / 5.4：
The Adjoint Operator / 6：
The Dual of a Banach Space / 6.1：
Weak Convergence / 6.3：
Hilbert Space / 6.4：
The Adjoint of a Bounded Linear Operator / 6.5：
Bounded Self-adjoint Operators -- Spectral Theory / 6.6：
The Adjoint of an Unbounded Linear Operator in Hilbert Space Problems / 6.7：
Linear Compact Operators / 7：
Examples of Compact Operators / 7.1：
The Fredholm Alternative / 7.3：
The Spectrum / 7.4：
Compact Self-adjoint Operators / 7.5：
The Numerical Solution of Linear Integral Equations Problems / 7.6：
Nonlinear Compact Operators and Monotonicity / 8：
The Schauder Fixed Point Theorem / 8.1：
Positive and Monotone Operators in Partially Ordered Banach Spaces Problems / 8.3：
The Spectral Theorem / 9：
Background to the Spectral Theorem / 9.1：
The Spectral Theorem for Bounded Self-adjoint Operators / 9.4：
The Spectrum and the Resolvent / 9.5：
Unbounded Self-adjoint Operators / 9.6：
The Solution of an Evolution Equation Problems / 9.7：
Generalized Eigenfunction Expansions Associated with Ordinary Differential Equations / 10：
Extensions of Symmetric Operators / 10.1：
Formal Ordinary Differential Operators: Preliminaries / 10.3：
Symmetric Operators Associated with Formal Ordinary Differential Operators / 10.4：
The Construction of Self-adjoint Extensions / 10.5：
Generalized Eigenfunction Expansions Problems / 10.6：
Linear Elliptic Partial Differential Equations / 11：
Notation / 11.1：
Weak Derivatives and Sobolev Spaces / 11.3：
The Generalized Dirichlet Problem / 11.4：
Fredholm Alternative for Generalized Dirichlet Problem / 11.5：
Smoothness of Weak Solutions / 11.6：
Further Developments Problems / 11.7：
The Finite Element Method / 12：
The Ritz Method / 12.1：
The Rate of Convergence of the Finite Element Method Problems / 12.3：
Introduction to Degree Theory / 13：
The Degree in Finite Dimensions / 13.1：
The Leray-Schauder Degree / 13.3：
A Problem in Radiative Transfer Problems / 13.4：
Bifurcation Theory / 14：
Local Bifurcation Theory / 14.1：
Global Eigenfunction Theory Problems / 14.3：
References
List of Symbols
Index
Preface
Acknowledgements
Banach Spaces / 1：
38.
図書
Johann Schröder
39.
図書
Meir Smorodinsky
40.
図書
Leiba Rodman
41.
図書
K.O. Friedrichs
42.
図書
I. Erdelyi, editor
43.
図書
Marvin Rosenblum and James Rovnyak
出版情報:
New York : Oxford University Press , Oxford : Clarendon Press, 1985 xii, 161 p. ; 25 cm
シリーズ名:
Oxford mathematical monographs
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44.
図書
Raúl E. Curto, Palle E.T. Jørgensen, editors
出版情報:
Boston : Birkhäuser, c1994 vii, 360 p. ; 25 cm
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45.
図書
Barry Simon
46.
図書
Nikolai K. Nikolski ; translated by Andreas Hartmann
目次情報:
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Model operators and free interpolation: Contents Foreword to part C The basic function model
Elements of spectral theory in the language of the characteristic function
Decompositions into invariant subspaces and free interpolation
Analytic problems in linear system theory: Contents Foreword to part D Basic theory
First optimizations: Multiplicity of the spectrum and the DISC
Eigenvector decompositions, vector valued exponentials, and squared optimization
A glance at bases of exponentials and of reproducing kernels A brief
Introduction to $H^{\infty}$ control
Bibliography Author
Index Subject
Index Symbol
Index Errata to volume 1
Model operators and free interpolation: Contents Foreword to part C The basic function model
Elements of spectral theory in the language of the characteristic function
Decompositions into invariant subspaces and free interpolation
47.
図書
Y.A. Abramovich, C.D. Aliprantis
目次情報:
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Odds and ends Basic operator theory
Operators on $AL$- and $AM$-spaces
Special classes of operators
Integral operators Spectral properties
Some special spectra Positive matrices
Irreducible operators Invariant subspaces
The Daugavet equation
Bibliography
Index
Odds and ends Basic operator theory
Operators on $AL$- and $AM$-spaces
Special classes of operators
48.
図書
H. Garth Dales ... [et al.]
目次情報:
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Banach algebras / 1：
Harmonic analysis and amenability / 2：
Invariant subspaces / 3：
Local spectral theory / 4：
Single-valued extension property and Fredholm theory / 5：
Banach algebras / 1：
Harmonic analysis and amenability / 2：
Invariant subspaces / 3：
49.
図書
Michael I. Gilʹ
50.
図書
Joseph A. Ball ... [et al.], editors
51.
図書
edited by Ronald R. Yager, Janusz Kacprzyk and Gleb Beliakov
52.
図書
Mikhail S. Livshits and Artem A. Yantsevich ; translated by the American Mathematical Society ; edited and introduced by Ronald G. Douglas
出版情報:
Washington : V. H. Winston , New York : distributed solely by Halsted Press, 1979 xiii, 212 p. ; 22 cm
シリーズ名:
A Halsted Press book
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53.
図書
edited by I. Gohberg
54.
図書
Tuomas Hytönen ... [et al.]
55.
図書
by Béla Sz.-Nagy and Ciprian Foiaş
出版情報:
Amsterdam : North-Holland Pub. Co., 1970 xiii, 387 p. ; 24 cm
シリーズ名:
American Elsevier
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56.
ＥＢ
Heinz H. Bauschke, Regina S. Burachik, D. Russell Luke, editors
出版情報:
[Berlin] : SpringerLink, [20--] 1 online resource (xix, 489 p.)
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57.
図書
Gerard J. Murphy
出版情報:
Boston ; Tokyo : Academic Press, c1990 x, 286 p. ; 24 cm
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Elementary Spectral Theory
C*-Algebras and Hilbert Space Operators
Ideals and Positive Functionals
Von Neumann Algebras
Representations of C*-Algebras
Direct Limits and Tensor Products
K-Theory of C*-Algebras
Elementary Spectral Theory
C*-Algebras and Hilbert Space Operators
Ideals and Positive Functionals
58.
図書
Isabelle Chalendar, Jonathan R. Partington
目次情報:
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Preface
Background / 1：
Functional analysis / 1.1：
Weak topology / 1.1.1：
Hahn-Banach theorem / 1.1.2：
Stone-Weierstrass theorem / 1.1.3：
Banach-Steinhaus theorem / 1.1.4：
Complex measures / 1.1.5：
Riesz representation theorem / 1.1.6：
Geometry of Banach spaces / 1.1.7：
Operator theory / 1.2：
Basic definitions and spectral properties / 1.2.1：
Wold decomposition of an isometry / 1.2.2：
Riesz-Dunford functional calculus / 1.2.3：
The Poisson kernel / 1.3：
Hardy spaces / 1.4：
Inner and outer functions / 1.4.1：
Consequences of the inner-outer factorization / 1.4.2：
The theorems of Beurling and Wiener / 1.4.3：
The disc algebra / 1.4.4：
Reproducing kernels, Riesz bases and Carleson sequences / 1.4.5：
Functions of bounded mean oscillation / 1.4.6：
The Hilbert transform on the unit circle / 1.4.7：
Number Theory / 1.5：
The operator-valued Poisson kernel and its applications / 2：
The operator-valued Poisson kernel / 2.1：
The H$ functional calculus for absolutely continuous p-contractions / 2.2：
H$ functional calculus in a complex Banach space / 2.3：
Absolutely continuous elementary spectral measures / 2.4：
Exercises
Comments
The basis of the S. Brown method / 3：
The starting point / 3.1.1：
The class A / 3.1.2：
Factorization of log-integrable functions / 3.1.3：
Applications in harmonic analysis / 3.3：
Subnormal operators / 3.4：
Borelian functional calculus for normal operators / 3.4.1：
Invariant subspaces for subnormal operators / 3.4.2：
Surjectivity of continuous bilinear mapping / 3.5：
Polynomially bounded operators with rich spectrum / 3.5.1：
Apostol's theorem / 4.1：
Operators with a C2(T) functional calculus / 4.2：
The Colojoara-Foias, theorem / 4.2.2：
Zenger's theorem / 4.3：
Zenger's theorem and a factorization result / 4.3.1：
A stronger version of Zenger's theorem / 4.3.2：
Carleson's interpolation theorem / 4.4：
Approximation using Apostol sets / 4.5：
Approximation of integrable non-negative functions / 4.5.1：
Approximate eigenvalues / 4.5.2：
Invariant subspace results / 4.6：
Beurling algebras / 5：
Properties of Beurling algebras / 5.1：
Theorems of Wermer and Atzmon / 5.2：
Bishop operators / 5.3：
Davie's functional calculus / 5.3.1：
The point spectrum / 5.3.2：
Rational Bishop operators / 5.4：
Cyclic vectors / 5.4.1：
The lattice of invariant subspaces / 5.4.2：
Applications of a fixed-point theorem / 6：
Operators commuting with compact operators / 6.1：
Essentially self-adjoint operators / 6.2：
Preliminaries / 6.2.1：
Application to invariant subspaces / 6.2.3：
Minimal vectors / 7：
The basic definitions / 7.1：
Minimal vectors in Hilbert space / 7.2：
A general extremal problem / 7.3：
Approximation in Hilbert spaces / 7.3.1：
Approximation in reflexive Banach spaces / 7.3.2：
Application to hyperinvariant subspaces / 7.4：
The main theorem / 7.4.1：
Compact operators / 7.4.2：
Weighted composition operators / 7.4.3：
Weighted shifts / 7.4.4：
Universal operators / 7.4.5：
Construction of universal models / 8.1：
Bilateral weighted shifts / 8.2：
Composition operators / 8.3：
Universality of composition operators / 8.3.1：
Minimal subspaces and eigenfunctions / 8.3.2：
Moment sequences and binomial sums / 9：
Moment sequences / 9.1：
Operators on sequence spaces / 9.2：
Binomial sums / 9.3：
Proof of Theorem 9.3.1 / 9.3.1：
A technical refinement / 9.3.2：
Application to Banach algebras and invariant subspaces / 9.3.3：
Positive and strictly-singular operators / 10：
Ordered spaces and positive operators / 10.1：
Invariant subspaces for positive operators / 10.2：
Strictly singular operators / 10.3：
References
Index
Preface
Background / 1：
Functional analysis / 1.1：
59.
図書
Ronald G. Douglas
図書
ＥＢ
