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Traces and Determinants of Linear Operators

  • Book
  • © 2000

Overview

Authors:
  1. Israel Gohberg

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

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  2. Seymour Goldberg

    1. Silver Spring, USA

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  3. Nahum Krupnik

    1. Dept. of Mathematics and Computer Science, Bar Ilan University, IL - Ramat Gan, Israel

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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 116)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Introduction

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 1-3

  3. Finite Rank Operators

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 5-23

  4. Continuous Extension of Trace and Determinant

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 25-38

  5. First Examples

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 39-45

  6. Trace Class and Hilbert-Schmidt Operators in Hilbert Space

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 47-90

  7. Nuclear Operators in Banach Spaces

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 91-110

  8. The Fredholm Determinant

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 111-132

  9. Possible Values of Traces and Determinants. Perelson Algebras

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 133-141

  10. Inversion Formulas

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 143-157

  11. Regularized Determinants

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 159-168

  12. Hilbert-Carleman Determinants

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 169-186

  13. Regularized Determinants of Higher Order

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 187-200

  14. Inversion Formulas via Generalized Determinants

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 201-211

  15. Determinants of Integral Operators with Semi-separable Kernels

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 213-242

  16. Algebras without the Approximation Property

    • Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 243-248

  17. Back Matter

    Pages 249-258
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Keywords

About this book

The authors initially planned to write an article describing the origins and devel­ opments of the theory of Fredholm operators and to present their recollections of this topic. We started to read again classical papers and we were sidetracked by the literature concerned with the theory and applications of traces and determi­ nants of infinite matrices and integral operators. We were especially impressed by the papers of Poincare, von Koch, Fredholm, Hilbert and Carleman, as well as F. Riesz's book on infinite systems of linear equations. Consequently our plans were changed and we decided to write a paper on the history of determinants of infi­ nite matrices and operators. During the preparation of our paper we realized that many mathematical questions had to be answered in order to gain a more com­ plete understanding of the subject. So, we changed our plans again and decided to present the subject in a more advanced form which would satisfy our new require­ ments. This whole process took between four and five years of challenging, but enjoyable work. This entailed the study of the appropriate relatively recent results of Grothendieck, Ruston, Pietsch, Hermann Konig and others. After the papers [GGK1] and [GGK2] were published, we saw that the written material could serve as the basis of a book.

Authors and Affiliations

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

    Israel Gohberg

  • Silver Spring, USA

    Seymour Goldberg

  • Dept. of Mathematics and Computer Science, Bar Ilan University, IL - Ramat Gan, Israel

    Nahum Krupnik

Bibliographic Information

  • Book Title: Traces and Determinants of Linear Operators

  • Authors: Israel Gohberg, Seymour Goldberg, Nahum Krupnik

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-8401-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Hardcover ISBN: 978-3-7643-6177-8Published: 14 February 2000

  • Softcover ISBN: 978-3-0348-9551-4Published: 29 October 2012

  • eBook ISBN: 978-3-0348-8401-3Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: IX, 258

  • Topics: Analysis

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