Indefinite Inner Product Spaces [Paperback]

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.lc8