A perturbation characterization of compactness of self-adjoint operators

Tom 158 / 2003

Heydar Radjavi, Ping-Kwan Tam, Kok-Keong Tan Studia Mathematica 158 (2003), 199-205 MSC: Primary 47B07, 47A55. DOI: 10.4064/sm158-3-1

Streszczenie

A characterization of compactness of a given self-adjoint bounded operator $A$ on a separable infinite-dimensional Hilbert space is established in terms of the spectrum of perturbations. An example is presented to show that without separability, the perturbation condition, which is always necessary, is not sufficient. For non-separable spaces, another condition on the self-adjoint operator $A$, which is necessary and sufficient for the perturbation, is given.

Autorzy

  • Heydar RadjaviDepartment of Mathematics and Statistics
    Dalhousie University
    Halifax, Nova Scotia, Canada, B3H 3J5
    e-mail
  • Ping-Kwan TamDepartment of Mathematics
    Chinese University of Hong Kong
    Shatin, New Territories, Hong Kong
    e-mail
  • Kok-Keong TanDepartment of Mathematics and Statistics
    Dalhousie University
    Halifax, Nova Scotia, Canada, B3H 3J5
    e-mail

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