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AuthorBognรกr, Jรกnos. author
TitleIndefinite Inner Product Spaces [electronic resource] / by Jรกnos Bognรกr
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1974
Connect tohttp://dx.doi.org/10.1007/978-3-642-65567-8
Descript X, 226 p. online resource

CONTENT

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 -- 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 -- 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 -- 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 ?kยท 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


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