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Birkhäuser

Classes of Linear Operators

  • Book
  • © 1993

Overview

Authors:
  1. Israel Gohberg

    1. School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

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  2. Marinus A. Kaashoek

    1. Faculteit Wiskunde en Informatica, Vrije Universiteit, Amsterdam, The Netherlands

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    You can also search for this author in PubMed   Google Scholar

  3. Seymour Goldberg

    1. Department of Mathematics, University of Maryland, College Park, USA

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 63)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    1. Introduction

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 469-470

  3. Triangular Representations

    1. Front Matter

      Pages 471-471
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    2. Additive Lower-Upper Triangular Decompositions of Operators

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 472-501

    3. Operators in Triangular Form

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 502-512

    4. Multiplicative Lower-Upper Triangular Decompositions of Operators

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 513-560

  4. Classes of Toeplitz Operators

    1. Front Matter

      Pages 561-561
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    2. Block Toeplitz Operators

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 562-582

    3. Toeplitz Operators Defined by Rational Matrix Functions

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 583-622

    4. Toeplitz Operators Defined by Piecewise Continuous Matrix Functions

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 623-651

  5. Contractive Operators and Characteristic Operator Functions

    1. Front Matter

      Pages 653-653
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    2. Block Shift Operators

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 654-664

    3. Dilation Theory

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 665-699

    4. Unitary Systems and Characteristic Operator Functions

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 700-786

  6. Banach Algebras and Algebras of Operators

    1. Front Matter

      Pages 787-787
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    2. General Theory

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 788-810

    3. Commutative Banach Algebras

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 811-842

    4. Elements of C*-Algebra Theory

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 843-869

    5. Banach Algebras Generated by Toeplitz Operators

      • I. Gohberg, M. A. Kaashoek, S. Goldberg
      Pages 870-890

  7. Extension and Completion Problems

    1. Front Matter

      Pages 891-891
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Keywords

About this book

These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.

Authors and Affiliations

  • School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    Israel Gohberg

  • Faculteit Wiskunde en Informatica, Vrije Universiteit, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  • Department of Mathematics, University of Maryland, College Park, USA

    Seymour Goldberg

Bibliographic Information

  • Book Title: Classes of Linear Operators

  • Authors: Israel Gohberg, Marinus A. Kaashoek, Seymour Goldberg

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8558-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 1993

  • Hardcover ISBN: 978-3-7643-2944-0Published: 01 October 1993

  • Softcover ISBN: 978-3-0348-9679-5Published: 01 November 2012

  • eBook ISBN: 978-3-0348-8558-4Published: 09 March 2013

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 556

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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