Advertisement

Traces and Determinants of Linear Operators

  • Israel Gohberg
  • Seymour Goldberg
  • Nahum Krupnik

Part of the Operator Theory Advances and Applications book series (OT, volume 116)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 1-3
  3. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 5-23
  4. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 25-38
  5. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 39-45
  6. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 47-90
  7. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 91-110
  8. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 111-132
  9. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 133-141
  10. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 143-157
  11. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 159-168
  12. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 169-186
  13. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 187-200
  14. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 201-211
  15. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 213-242
  16. Israel Gohberg, Seymour Goldberg, Nahum Krupnik
    Pages 243-248
  17. Back Matter
    Pages 249-258

About this book

Introduction

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.

Keywords

Eigenvalue Hilbert space approximation property banach spaces integral integral equation linear algebra operator operator theory

Authors and affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Nahum Krupnik
    • 3
  1. 1.School of Mathematical Sciences, Raymond and Beverly Sackler, Faculty of Exact SciencesTel Aviv UniversityIL - Ramat AvivIsrael
  2. 2.Silver SpringUSA
  3. 3.Dept. of Mathematics and Computer ScienceBar Ilan UniversityIL - Ramat GanIsrael

Bibliographic information