Preface
Notation and Terminology
    0.1  Notation
    0.2  Terminology
Part 1 EXERCISES ET AL
  Chapter 1 Normed Vector Spaces.Banach Spaces
    1.1  Basics
      1.1.1  Definitions and Examples
      1.1.2  Operations on Banach Spaces
      1.1.3  Convex Sets
      1.1.4  LP-Spaces
    1.2  True or False: Questions
    1.3  Exercises with Solutions
    1.4  Tests
    1.5  More Exercises
  Chapter 2 Bounded Linear Operators on Banach Spaces
    2.1  Basics
      2.1.1  Basic Definitions
      2.1.2  Dual Spaces
      2.1.3  The Fourier Transform
      2.1.4  Invertibility
      2.1.5  Series in Banach Spaces
      2.1.6  Neumann Series
      2.1.7  Operator-Valued Analytic Functions
      2.1.8  The Four Pillars of Functional Analysis
    2.2  True or False: Questions
    2.3  Exercises with Solutions
    2.4  Tests
    2.5  More Exercises
  Chapter 3 Hilbert Spaces
    3.1  Basics
      3.1.1  Definitions and Examples
      3.1.2  Modes of Convergence of Sequences
      3.1.3  Orthogonality
      3.1.4  The Closest Point Property and the Projection Theorem
      3.1.5  Orthonormal Sets and Basy ana tne rro
      3.1.6  Orthogonal Polynomials
      3.1.7  Linear Operators on a Hilbert Space
      3.1.8  Operator Topologies
    3.2  True or False: Questions
    3.3  Exercises with Solutions
    3.4  Tests
    3.5  More Exercises
  Chapter 4 Classes of Linear Operators on Hilbert Spaces 99
    4.1  Basics
      4.1.1  Operator Theory Basics
      4.1.2  Cartesian Form
      4.1.3  Operator Matrices
      4.1.4  A Word on the Invariant Subspace Problem
    4.2  True or False: Questions
    4.3  Exercises with Solutions
    4.4  Tests
    4.5  More Exercises
  Chapter 5 Positive Operators.Square Root
    5.1  Basics
      5.1.1  Positive Operators
      5.1.2  Invertibility Revisited
      5.1.3  Square Root of Positive Operators
    5.2  True or False: Questions
    5.3  Exercises with Solutions
    5.4  Tests
    5.5  More Exercises
  Chapter 6 Absolute Value.Polar Decomposition of an Operator
    6.1  Basics
      6.1.1  Definitions and Properties
      6.1.2  The Absolute Value and the Product
      6.1.3  The Absolute Value and the Sum
      6.1.4  The Absolute Value and Other Inequalities
      6.1.5  Polar Decomposition
    6.2  True or False: Questions
    6.3  Exercises with Solutions
    6.4  Tests
    6.5  More Exercises
  Chapter 7 Spectrum of an Operator
    7.1  Basics
      7.1.1  Definitions and Properties
      7.1.2  The Resolvent Function
      7.1.3  Subsets of the Spectrum
      7.1.4  Spectrum of the Product of Operators
      7.1.5  On The Operator Equation AX - XB = C
      7.1.6  Polynomial Calcul-yuawva A
    7.2  True or False: Questions
    7.3  Exercises with Solutions
    7.4  Tests
    7.5  More Exercises
  Chapter 8 Spectral Radius Numerical Range
    8.1  Basics
      8.1.1  Spectral Radius
      8.1.2  Numerical Range
    8.2  True or False: Questions
    8.3  Exercises with Solutions
    8.4  Tests
    8.5  More Exercises
  Chapter 9 Compact Operators
    9.1  Basics
      9.1.1  Compact Operators
      9.1.2  Hilbert-Schmidt Operators
      9.1.3  Spectrum and Compact Operators
    9.2  True or False: Questions
    9.3  Exercises with Solutions
    9.4  Tests
    9.5  More Exercises
  Chapter 10 Closed Operators
    10.1  Basics
      10.1.1  Spectrum
      10.1.2  Closedness of Products and Sums
      10.1.3  A Word on Distributional Derivatives
    10.2  True or False: Questions
    10.3  Exercises with Solutions
    10.4  Tests
    10.5  More Exercises
  Chapter 11 Functional Calculi
    11.1  Basics
      11.1.1  Functional Calculus for Self-adjoint Operators
      11.1.2  Functional Calculus for Normal Operators
      11.1.3  A Little Digression
      11.1.4  The Fuglede-Putnam Theorem Revisited
      11.1.5  The Beck-Putnam Theorem
    11.2  True or False: Questions
    11.3  Exercises with Solutions
    11.4  Tests
    11.5  More Exercises
  Chapter 12 Hyponormal Operators
    12.1  Basics
    12.2  True or False: Questions
    12.3  Exercises with Solutions
    12.4  Tests
    12.5  More Exercises
  Chapter 13 Similarities of Operators
    13.1  Important Theorems
      13.1.1  The Berberian Theorem
      13.1.2  The Williams Theorem
      13.1.3  The Embry Theorem
    13.2  Exercises with Solutions
    13.3  Tests
    13.4  More Exercises
Part 2 SOLUTIONS
  Chapter 1 Normed Vector Spaces Banach Spaces
    1.2  True or False: Answers
    1.3  Solutions to Exercises
    1.4  Hints/Answers to Tests
  Chapter 2 Bounded Linear Operators on Banach Spaces
    2.2  True or False: Answers
    2.3  Solutions to Exercises
    2.4  Hints/Answers to Tests
  Chapter 3 Hilbert Spaces
    3.2  True or False: Answers
    3.3  Solutions to Exercises
    3.4  Hints/Answers to Tests
  Chapter 4 Classes of Linear Operators on Hilbert Spaces 377
    4.2  True or False: Answers
    4.3  Solutions to Exercises
    4.4  Hints/Answers to Tests
  Chapter 5 Positive Operators Square Root
    5.2  True or False: Answers
    5.3  Solutions to Exercises
    5.4  Hints/Answers to Tests
  Chapter 6 Absolute Value Polar Decomposition of an Operator
    6.2  True or False: Answers
    6.3  Solutions to Exercises
    6.4  Hints/Answers to Tests
  Chapter 7 Spectrum of an Operator
    7.2  True or False: Answers
    7.3  Solutions to Exercises
    7.4  Hints/Answers to Tests
  Chapter 8 Spectral Radius Numerical Range
    8.2  True or False: Answers
    8.3  Solutions to Exercises
    8.4  Hints/Answers to Tests
  Chapter 9 Compact Operators
    9.2  True or False: Answers
    9.3  Solutions to Exercises
    9.4  Hints/Answers to Tests
  Chapter 10 Closed Operators
    10.2  True or False: Answers
    10.3  Solutions to Exercises
    10.4  Hints/Answers to Tests
  Chapter 11 Functional Calculi
    11.2  True or False: Answers
    11.3  Solutions to Exercises
    11.4  Hints/Answers to Tests
  Chapter 12 Hyponormal Operators
    12.2  True or False: Answers
    12.3  Solutions to Exercises
    12.4  Hints/Answers to Tests
  Chapter 13 Similarities of Operators
    13.2  Solutions to Exercises
    13.3  Hints/Answers to Tests
Bibliography
Index
编辑手记