Indefinite Inner Product Spaces
| Main Author: | |
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974, 1974
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| Edition: | 1st ed. 1974 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 5. Quadratic Operator Equations in I-Iilbert Space
- 6. Spectral Functions
- Notes to Chapter VIII
- IX. Pontrjagin Spaces and Their Linear Operators
- 1. The Spaces ?k· Positive Subspaces
- 2. Closed Subspaces
- 3. Isometric Operators: Continuity
- 4. Isometric and Symmetric Operators: Number and Length of Jordan Chains
- 5. Proof of Theorem 4.3
- 6. Regular Symmetric Extensions
- 7. Invariant Positive Subspaces: Existence
- 8. Invariant Positive Subspaces: Uniqueness
- 9. Common Invariant Positive Subspaces for Commuting Operators
- Notes to Chapter IX
- Index of Terms
- Index of Symbols
- 2. Partial Majorants. The Weak Topology
- 3. Metrizable Partial Majorants
- 4. The Polar of a Normed Partial Majorant
- 5. Admissible Topologies
- 6. Orthogonal Companions and Admissible Topologies
- 7. Projections and Admissible Topologies
- 8. Intrinsic Topology
- 9. Projections and Intrinsic Topology
- Notes to Chapter III
- IV. Majorant Topologies on Inner Product Spaces
- 1. Majorants
- 2. Majorants and Metrizable Partial Majorants
- 3. Orthonormal Systems
- 4. Minimal Majorants
- 5. Majorants and Decomposability
- 6. Decomposition Majorants
- 7. Invariant Properties of E+ and E-
- 8. Subspaces of Spaces with a Hilbert Majorant
- Notes to Chapter IV
- V. The Geometry of Krein Spaces
- 1. Krein Spaces
- 2. Krein Spaces as Completions
- 3. Subspaces
- 4. Maximal Semi-definite Subspaces
- 5. Uniformly Definite Subspaces
- 6.Non-uniformly Definite Subspaces
- 7. Maximal Uniformly Definite Subspaces
- 8. Regular and Singular Subspaces
- I. Inner Product Spaces without Topology
- 1. Vector Spaces
- 2. Inner Products
- 3. Orthogonality
- 4. Isotropic Vectors
- 5. Maximal Non-degenerate Subspaces
- 6. Maximal Semi-definite Subspaces
- 7. Maximal Neutral Subspaces
- S. Projections of Vectors on Subspaces
- 9. Ortho-complemented Subspaces
- 10. Dual Pairs of Subspaces
- 11. Fundamental Decompositions
- Notes to Chapter I
- II. Linear Operators in Inner Product Spaces without Topology
- 1. Linear Operators in Vector Spaces
- 2. Isometric Operators
- 3. Symmetric Operators
- 4. Cayley Transformations
- 5. Principal Vectors of Cayley Transforms
- 6. Pairs of Inner Products: Semi-boundedness
- 7. Pairs of Inner Products: Sign
- 8. Plus-operators
- 9. Pesonen Operators
- 10. Fundamental Projectors
- 11. Fundamental Symmetries. Angular Operators
- Notes to Chapter II
- III. Partial Majorants and Admissible Topologies on Inner Product Spaces
- 1. Locally Convex Topologies on Vector Spaces
- 9. Alternating Pairs
- 10. Dissipative Operators in Hilbert Space
- Notes to Chapter V
- VI. Unitary and Selfadjoint Operators in Krein Spaces
- 1. Preliminaries
- 2. The Adjoint of an Operator
- 3. Isometric Operators
- 4. Unitary and Rectangular Isometric Operators
- 5. Spectral Properties of Unitary Operators
- 6. Selfadjoint Operators
- 7. Cayley Transformations
- 8. Unitary Dilations
- Notes to Chapter VI
- VII. Positive Operators and Plus-operators in Krein Spaces
- 1. Positive Operators
- 2. Operators of the Form T*T
- 3. Uniformly Positive Operators
- 4. Plus-operators
- 5. Strict Plus-operators
- 6. Doubly Strict Plus-operators
- Notes to Chapter VII
- VIII. Invariant Semi-definite Subspaces of Linear Operators in Krein Spaces
- 1. Fundamentally Reducible Operators
- 2. Invariant Positive Subspaces of Plus-operators
- 3. Invariant Semi-definite Subspaces of Unitary and Selfadjoint Operators
- 4. Quadratic Pencils of Operators in Hilbert Space