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1.

図書

図書
Y.A. Abramovich, C.D. Aliprantis
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiv, 530 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 50
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目次情報: 続きを見る
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
2.

図書

図書
Nikolai K. Nikolski ; translated by Andreas Hartmann
出版情報: Providence, R.I. : American Mathematical Society, c2002  xiv, 439 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 93 . Operators, functions, and systems : an easy reading ; v. 2
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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
3.

図書

図書
edited by Ronald R. Yager, Janusz Kacprzyk and Gleb Beliakov
出版情報: Berlin ; London : Springer, c2011  XIV, 295 p. ; 24 cm
シリーズ名: Studies in fuzziness and soft computing ; 265
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4.

図書

図書
Isabelle Chalendar, Jonathan R. Partington
出版情報: Cambridge, UK : Cambridge University Press, 2011  xi, 285 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 188
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目次情報: 続きを見る
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:
5.

図書

図書
Ioannis Antoniou and Günter Lumer (editors)
出版情報: Boca Raton, Fla. ; London : Chapman & Hall/CRC Press, c1999  378 p. ; 26 cm
シリーズ名: Research notes in mathematics ; 399
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6.

図書

図書
edited by Sheldon Axler, John E. McCarthy, Donald Sarason
出版情報: Cambridge ; New York : Cambridge University Press, 1998  ix, 476 p. ; 24 cm
シリーズ名: Mathematical Sciences Research Institute publications ; 33
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7.

図書

図書
by Vitalii G. Kurbatov
出版情報: Dordrecht ; Boston : Kluwer Academic Pub., c1999  xx, 432 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 473
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8.

図書

図書
H. Garth Dales ... [et al.]
出版情報: Cambridge : Cambridge University Press, 2003  xi, 324 p. ; 24 cm
シリーズ名: London Mathematical Society student texts ; 57
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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:
9.

図書

図書
Michael I. Gilʹ
出版情報: Berlin ; Tokyo : Springer-Verlag, c2003  xiv, 256 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1830
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10.

図書

図書
Joseph A. Ball ... [et al.], editors
出版情報: Basel : Birkhauser, c2004  xxii, 595 p. ; 24 cm
シリーズ名: Operator theory : advances and applications ; 149
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