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Hilbert Space Operators

A Problem Solving Approach

  • Textbook
  • © 2003

Overview

Authors:
  1. Carlos S. Kubrusly

    1. Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xv
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  2. Invariant Subspaces

    • Carlos S. Kubrusly
    Pages 1-11

  3. Hilbert Space Operators

    • Carlos S. Kubrusly
    Pages 13-22

  4. Convergence and Stability

    • Carlos S. Kubrusly
    Pages 23-32

  5. Reducing Subspaces

    • Carlos S. Kubrusly
    Pages 33-40

  6. Shifts

    • Carlos S. Kubrusly
    Pages 41-50

  7. Decompositions

    • Carlos S. Kubrusly
    Pages 51-64

  8. Hyponormal Operators

    • Carlos S. Kubrusly
    Pages 65-74

  9. Spectral Properties

    • Carlos S. Kubrusly
    Pages 75-92

  10. Paranormal Operators

    • Carlos S. Kubrusly
    Pages 93-108

  11. Proper Contractions

    • Carlos S. Kubrusly
    Pages 109-116

  12. Quasireducible Operators

    • Carlos S. Kubrusly
    Pages 117-128

  13. The Lomonosov Theorem

    • Carlos S. Kubrusly
    Pages 129-142

  14. Back Matter

    Pages 143-151
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Keywords

About this book

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.

Reviews

"…the author treats many new subjects of operator theory for graduate students and mathematicians, i.e., quasihyponormal operators, paranormal operators, proper contractions, quasireducible operators, a detailed presentation of the Lomonosov theorem on nontrivial hyperinvariant subspaces for compact operators, etc. This book will be of benefit to graduate students (in mathematics, physics, engineering, economics, and statistics) and many mathematicians."

—Zentralblatt MATH

"…many totally new subjects are offered to the potential reader…. The author has great teaching experience reflected by the skillful selection of background material, the gradual statements of the problems, and the detailed presentation of the solutions. The book is intended [for] an audience mainly formed by various types of graduate students: in mathematics, statistics, physics and, perhaps, in engineering and economics. It can be useful even for working mathematicians, as a reference book in a broad sense…."

—Mathematical Reviews

Authors and Affiliations

  • Catholic University of Rio de Janeiro, Rio de Janeiro, Brazil

    Carlos S. Kubrusly

Bibliographic Information

  • Book Title: Hilbert Space Operators

  • Book Subtitle: A Problem Solving Approach

  • Authors: Carlos S. Kubrusly

  • DOI: https://doi.org/10.1007/978-1-4612-2064-0

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2003

  • Softcover ISBN: 978-0-8176-3242-7Published: 07 August 2003

  • eBook ISBN: 978-1-4612-2064-0Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XIII, 149

  • Topics: Operator Theory, Functional Analysis, Mathematical Methods in Physics

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