Invertibility and Singularity for Bounded Linear Operators by Robin Harte -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Contents Prologue Preface to the First Edition 1. Normed Linear Spaces

1.1 Norms or length functions 1.2 Metric and topology 1.3 Translation invariance 1.4 Subspaces and quotients 1.5 The Riesz lemmas 1.6 Cartesian products 1.7 Isometry and equivalence 1.8 Sequence and function spaces 1.9 Enlargements 1.10 Normed linear algebras 1.11 Partially ordered spaces

2. Bounded Linear Operators

2.1 Continuity of linear operators 2.2 The normed space of bounded operators 2.3 Subspaces and quotients 2.4 Cartesian products 2.5 Projections 2.6 Sequence and function spaces 2.7 Enlargements 2.8 Shift operators 2.9 Composition operators 2.10 Normed linear algebras 2.11 Partially ordered spaces

3. Invertibility and Singularity

3.1 Invertibility and isomorphism 3.2 Monomorphisms and epimorphisms 3.3 Boundedness below 3.4 Openness 3.5 Boundary mappings 3.6 Left and right invertibility 3.7 Almost invertible operators 3.8 Regular operators 3.9 Essential invertibility 3.10 Algebraic invertibility 3.11 Subspaces, quotients, and products 3.12 Sequence and function spaces

4. Banach Spaces and Completeness

4.1 Cauchy sequences 4.2 Completeness 4.3 Spaces of functions and operators 4.4 Extension by continuity 4.5 Completions 4.6 The open mapping theorem 4.7 Almost open and onto mappings 4.8 Complemented subspaces 4.9 Uniform boundedness

5. Linear Functionals and Duality

5.1 The dual space and the dual operator 5.2 Poles and polars 5.3 The Hahn-Banach theorem 5.4 Duality theory 5.5 The separation theorem 5.6 Composition operators 5.7 Enlargements 5.8 Sequence and function spaces 5.9 The second dual 5.10 An uncomplemented subspace 5.11 Extreme points 5.12 Differential calculus

6. Finite Dimensional Spaces and Compactness

6.1 Linear dependence and independence 6.2 Finite dimensional spaces 6.3 Operators of finite rank 6.4 Fredholm operators 6.5 Weyl operators and the index 6.6 Compactness and total boundedness 6.7 Essential enlargement 6.8 Compact operators 6.9 Semi-Fredholm operators 6.10 Almost Fredholm operators 6.11 Completeness 6.12 Duality theory 6.13 Composition operators

7. Operator Algebra and Commutivity

7.1 Commutants and double commutants 7.2 Maximal ideals and the radical 7.3 Regularity 7.4 Quasinilpotent elements 7.5 Polar and quasipolar elements 7.6 Homomorphisms and Fredholm theory 7.7 Browder operators 7.8 Ascent and descent 7.9 Semi-Browder operators 7.10 Connectedness and homotopy 7.11 Generalized exponentials 7.12 Continuous functions 7.13 Linear functionals and states

8. Inner Products and Orthogonality

8.1 Inner products 8.2 Orthogonality 8.3 The nearest point theorem 8.4 Completeness 8.5 Duality 8.6 Positive operators 8.7 Regularity 8.8 Hilbert algebra 8.9 Enlargements

9. Liouville’s Theorem and Spectral Theory

9.1 Liouville’s theorem 9.2 The spectrum 9.3 The spectral boundary 9.4 Subalgebras and quotients 9.5 The spectral radius 9.6 Gelfand’s theorem 9.7 The functional calculus 9.8 Essential spectra 9.9 Hilbert algebra 9.10 States and representations

10. Comparison of Operators and Exactness

10.1 Majorization and factorization 10.2 Mixed interpolation 10.3 Exactness 10.4 Composition operators and duality 10.5 Enlargement and completion 10.6 Essential exactness 10.7 Algebraic exactness 10.8 Hilbert spaces 10.9 Skew exactness

11. Multiparameter Spectral Theory

11.1 Left and right spectra 11.2 Polynomials 11.3 The spectral mapping theorem 11.4 Many variables 11.5 The Silov boundary 11.6 Composition operators 11.7 Tensor products 11.8 Quasicommuting systems 11.9 The Taylor spectrum 11.10 Algebraic and essential spectra 11.11 Functional calculus

Epilogue Notes, Comments, and Exercises References Notation Index