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Integral Equations and Operator Theory

, Volume 27, Issue 1, pp 10–47 | Cite as

Hilbert-Carleman and regularized determinants for linear operators

  • Israel Gohberg
  • Seymour Goldberg
  • Naum Krupnik
Article

Abstract

A general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed. In this approach regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators. We characterize the algebras for which such extensions exist, describe the main properties of the extended determinants, obtain Cramer's rule and the formulas for the resolvent which are expressed via the extended tracestr(A k ) of iterations and regularized determinants.

This paper is a continuation of the paper [GGKr].

MSC 1991

47B53 

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Copyright information

© Birkhäuser Verlag 1997

Authors and Affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Naum Krupnik
    • 3
  1. 1.School of Mathematics Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Dept. of Math. and Comp. ScienceBar-Ilan UniversityRamat-GanIsrael

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