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9780691095691

An Introduction to Linear Transformations in Hilbert Space

by
  • ISBN13:

    9780691095691

  • ISBN10:

    0691095698

  • Format: Paperback
  • Copyright: 1941-12-31
  • Publisher: Princeton Univ Pr

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Table of Contents

Preface
Table of Contents
Introduction
1(3)
Hilbert Space
4(18)
The Postulates
4(2)
Linear Normed Spaces
6(1)
Additivity and Continuity
7(4)
Linear Functionals
11(3)
Linear Manifolds
14(2)
Orthonormal Sets
16(6)
Realizations of Hilbert Space
22(9)
Preliminary Considerations
22(1)
l2
23(3)
h1 hn and h1 h2
26(1)
L2
27(4)
Additive and Closed Transformations
31(14)
The Graph of a Transformation
31(3)
Adjoints and Closure
34(4)
Symmetric and Self-adjoint Operators
38(4)
C.a.d.d. Transformations
42(3)
Weak Convergence
45(6)
Weak Completeness
45(2)
Weak Compactness
47(1)
Closed Transformations with Domain h
48(3)
Projections and Isometry
51(13)
Projections
51(5)
Unitary and Isometric Transformations
56(4)
Partially Isometric Transformations
60(2)
C.a.d.d. Operators
62(2)
Resolutions of the Identity
64(17)
Self-adjoint Transformations with H Finite Dimensional
64(3)
Resolutions of the Identity and Integration
67(6)
Improper Integrals
73(4)
Commutativity and Normal Operators
77(4)
Bounded Self-Adjoint and Unitary Transformations
81(14)
Functions of a Bounded H
81(4)
(Hf, g)
85(3)
Integral Representation of a bounded H
88(1)
Integral Representation of a Unitary Operator
89(6)
Canonical Resolution and Integral Representations
95(15)
The Canonical Resolution
95(5)
Self-adjoint Operators
100(2)
Normal Operators
102(8)
Symmetric Operators
110(12)
The Cayley Transform
110(6)
Structure and Existence of Maximal Symmetric Operators
116(6)
References to Further Developments
122(8)
Spectrum
122(1)
Operational Calculus
123(1)
Commutativity and Normal Operators
124(1)
Symmetric Transformations
125(1)
Infinite Matrices
125(1)
Operators of Finite Norms
126
Stone's Theorem
125(2)
Rings of Operators
127(3)
References to Applications
130
Integral and Other Types of Operators
130
Differential Operators
130
Quantum Mechanics
131
Classical Mechanics
131

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