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Hilbert Space Operators

A Problem Solving Approach

  • Carlos S. Kubrusly

Table of contents

  1. Front Matter
    Pages i-xv
  2. Carlos S. Kubrusly
    Pages 1-11
  3. Carlos S. Kubrusly
    Pages 13-22
  4. Carlos S. Kubrusly
    Pages 23-32
  5. Carlos S. Kubrusly
    Pages 33-40
  6. Carlos S. Kubrusly
    Pages 41-50
  7. Carlos S. Kubrusly
    Pages 51-64
  8. Carlos S. Kubrusly
    Pages 65-74
  9. Carlos S. Kubrusly
    Pages 75-92
  10. Carlos S. Kubrusly
    Pages 93-108
  11. Carlos S. Kubrusly
    Pages 109-116
  12. Carlos S. Kubrusly
    Pages 117-128
  13. Carlos S. Kubrusly
    Pages 129-142
  14. Back Matter
    Pages 143-151

About this book

Introduction

This is a problem book on Hilbert space operators (Le. , on bounded linear transformations of a Hilbert space into itself) where theory and problems are investigated together. We tre!l:t only a part of the so-called single operator theory. Selected prob­ lems, ranging from standard textbook material to points on the boundary of the subject, are organized into twelve chapters. The book begins with elementary aspects of Invariant Subspaces for operators on Banach spaces 1. Basic properties of Hilbert Space Operators are introduced in in Chapter Chapter 2, Convergence and Stability are considered in Chapter 3, and Re­ ducing Subspaces is the theme of Chapter 4. Primary results about Shifts on Hilbert space comprise Chapter 5. These are introductory chapters where the majority of the problems consist of auxiliary results that prepare the ground for the next chapters. Chapter 6 deals with Decompositions for Hilbert space contractions, Chapter 7 focuses on Hyponormal Operators, and Chapter 8 is concerned with Spectral Properties of operators on Banach and Hilbert spaces. The next three chapters (as well as Chapter 6) carry their subjects from an introductory level to a more advanced one, including some recent results. Chapter 9 is about Paranormal Operators, Chapter 10 covers Proper Contractions, and Chapter 11 searches through Quasi­ reducible Operators. The final Chapter 12 commemorates three decades of The Lomonosov Theorem on nontrivial hyperinvariant subspaces for compact operators.

Keywords

Applied Mathematics Finite Hilbert space Invariant Operator theory Problem-solving algebra equation function functional analysis ksa mathematics proof theorem

Authors and affiliations

  • Carlos S. Kubrusly
    • 1
  1. 1.Catholic University of Rio de JaneiroRio de JaneiroBrazil

Bibliographic information