Indefinite Inner Product Spaces

Main Author: Bognar, J.
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1974, 1974
Edition:1st ed. 1974
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, A Series of Modern Surveys in Mathematics
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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
  • 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
  • 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