- 巴拿赫代数在算子理论中的应用(第2版影印版)
- - 作者：(美)R.G.道格拉斯|责编:高蓉//李黎
  - 出版社：世界图书出版公司
  - ISBN：9787506259620
  - 出版日期：2003/06/01
  - 页数：194
- 售价：23.6

内容大纲
本书讲述了Banach代数在算子理论中的应用，内容包括Banach空间的基本理论、可支配的Banach代数的基本性质、Hilbert空间上的几何学、紧算子和Fredhlom算子的性质、Hardy空间理论及Toephitz算子性质等。
作者介绍
目录
Preface to the Second Edition
Preface to the First Edition
Acknowledgments
Symbols and Notation
1 Banach Spaces
  1 The Banach Space of Continuous Functions
  2 Abstract Banach Spaces
  3 The Conjugate Space of Continuous Linear Functionals
  4 Examples of Banach spaces: co， l， and l
  5 Weak Topologies on Banach Spaces
  6 The Alaoglu Theorem
  7 The Hahn-Banach Theorem
  8 The Conjugate Space of C([0， 1])
  9 The Open Mapping Theorem
  10 The Lebesgue Spaces: Ll and L
  11 The Hardy Spaces: Hl and H
    Notes
    Exercises
2 Banach Algebras
  1 The Banach Algebra of Continuous Functions
  2 Abstract Banach Algebras
  3 Abstract Index in a banach Algebra
  4 The Space of Multiplicative Linear Functions
  5 The Gelfand Transform
  6 The Gelfand-Mazur Theorem
  7 The Gelfand Theorem for Commutative Banach Algebras
  8 The Spectral Radius Formula
  9 The Stone-Weierstrass Theorem
  10 The Generalized Stone-Weierstrass Theorem
  11 The Disk Algebra
  12 The Algebra of Functions with Absolutey Convergent Fourier series
  13 the Algebra of Bounded Measurable Functions
    Notes
    exercises
3 Geometry of Hilbert Space
  l Inner Product Spaces
  2 The Cauchy-Schwarz Inequality
  3 The Pythagorean Theorem
  4 Hilbert Spaces
  5 Examples of Hilbert Spaces：Cn，l2，L2，and H2
  6 The Riesz Representation Theorem
  7 The Existenee of Orthonormal Bases
  8 The Dimension Of Hilbert Spaces
    Notes
    Exercises
4 Operators on Hilbert Space and C*-Algebras
  1 The Adjoint Operator
  2 Normal and Self-adjoint Operators
  3 Proiections and Subspaces
  4 Multiplication Operators and Maximal Abelian Algebras

  5 rnle Bilateral Shift Operator
  6 C*-Algebras
  7 The Gelfand-Naimark Theorem
  8 The Spectral Theorem
  9 The Funcfional Calculus
  10 The Square Root of Positive Operators
  11 The Unilateral Shift Operator
  12 The Po1ar Decomposition
  13 Weak and Strong Operator Topologies
  14 W*-Algebras
  15 Isomorphisms of L-Spaces
  16 Normal Operators with Cycfic Vectors
  17 Maximal Abelian W*-Algebras
  18 *-Homomorphisms of C*-Algebras
  19 The Extended Functional Calculus
  20 The Fuglede Theorem
    Notes
    Exercises
5 Compact Operators，Fredholm Operators，and Index Theory
  l The Ideals of Finite Rank and Compact Operators
  2 Approximation of Compact Operators
  3 Examples of Compact Operators: Integral Operators
  4 The Calkin Algebra and Frcdholm Operators
  5 Atkinson's Theorem
  6 The Index of Frcdholm Operators
  7 The Fredholm Altemative
  8 Volterra Integral Operators
  9 Connectedness of the Unitary Group in a W*-Algebras
  10 Characterization of Index
  1l Quotient C*-Algebras
  12 Representations of the C*-Algebra of Compact Operators
    Notes
    Exercises
6 The Hardy Spaces
  l The Hardy Spaces: Hl, H2, and H
  2 Reducing Subspaces of Unitary Operators
  3 Beurling's Theorem
  4 The F. and M.Riesz Theorem
  5 The Maximal Ideal Space of H
  6 The Inner-Outer Factorization of Functions in H2
  7 The Modulus of Outer Functions
  8 The Conjugates of H1 and L/H0
  9 The Closedness of H+C
  10 Approximation by Quotients of Inner Functions
  11 The Gleason-Whitney Theorem
  12 Subalgebras between H and L
  13 Abstract Harmonic Extensions
  14 The Maximal Ideal Space of H+C
  15 The Invertibility of Functions in H+C
    Notes

    Exercises
7 Toeplitz Operators
  1 Toeplitz Operators
  2 The Spectral Inclusion Theorem
  3 The Symbol Map
  4 The Spectrum of Self-adjoint Toeplitz Operators
  5 The Spectrum of Analytic Toeplitz Operators
  6 The C*-Algebra Generated by the Unilateral Shift
  7 The Inverfibility of Toeplitz Operators witll Continuous Symbol
  8 The Invertibility of Unimodular Toeplitz Operators and Prediction Theory
  9 The Spectrum of Toeplitz Operators with Symbol in H+C
  10 The Connectedness of the Essenfial Spectrum
  11 Localization to the Centerofa C*-Algebra
  12 Locality of Fredholmness for Toeplitz Operators
    Notes
    Exercises
References
Index

内容大纲

作者介绍

目录

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