This book is an introduction to the subject and is devoted to standard material on linear functional analysis, and presents some ergodic theorems for classes of operators containing the quasi-compact operators. It discusses various classes of operators connected with the numerical range.
Table of Contents
1. Preliminaries: Set Theory and General Topology 2. Banach Spaces 3. Hilbert Spaces 4. Banach Algebras 5. Spectral Representation of Operators on Hilbert Spaces 6. The Numerical Range 7. Nonnormal Classes of Operators 8. Conditions Implying Normality 9. Symmetrizable Operators: Generalizations and Applications 10. Invariant Subspaces and Some Structure Theorems 11. The Weyl Spectrum of an Operator 12. Analytic and Quasi-Analytic Vectors 13. Schwarz Norms 14. Maximum Theorems for Operator-Valued Holomorphic 15. Uniform Ergodic Theorems for Some Classes of Operators