ABSTRACT

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.

chapter Chapter 1|18 pages

Preliminaries: Set Theory and General Topology

chapter Chapter 2|90 pages

Banach Spaces

chapter Chapter 3|33 pages

Hilbert Spaces

chapter Chapter 4|32 pages

Banach Algebras

chapter Chapter 5|26 pages

Spectral Representation of Operators on Hilbert Spaces

chapter Chapter 6|65 pages

The Numerical Range

chapter Chapter 7|45 pages

Nonnormal Classes of Operators

chapter Chapter 8|34 pages

Conditions Implying Normality

chapter Chapter 10|32 pages

Inveriant Subspaces and Some Structure Theorems

chapter Chapter 11|32 pages

The Weyl Spectrum of An Operator

chapter Chapter 12|24 pages

Analytic and Quasi-Analytic Vectors

chapter Chapter 13|15 pages

Schwarz Norms

chapter Chapter 15|12 pages

Uniform Ergodic Theorems for Some Classes of Operators