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Hilbert-Schmidt Operators

  • Israel Gohberg
  • Seymour Goldberg
  • Marinus A. Kaashoek
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 49)

Abstract

This chapter concerns another important set of compact operators, namely the Hilbert-Schmidt operators. The class of Hilbert-Schmidt operators has a natural Hilbert space structure and it contains the trace class operators. In the first section some additional properties of s-numbers are derived. In the second section the Hilbert-Schmidt operators are introduced and their main properties are established. The last section contains a completeness theorem for eigenvectors and generalized eigenvectors of Hilbert-Schmidt operators.

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Copyright information

© Springer Basel AG 1990

Authors and Affiliations

  • Israel Gohberg
    • 1
  • Seymour Goldberg
    • 2
  • Marinus A. Kaashoek
    • 3
  1. 1.School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact SciencesTel-Aviv UniversityTel-AvivIsrael
  2. 2.Department of MathematicsUniversity of MarylandCollege ParkUSA
  3. 3.Faculteit Wiskunde en InformaticaVrije UniversiteitAmsterdamThe Netherlands

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