Weyl's type theorems for algebraically w-hyponormal operators

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let T be a bounded linear operator acting on a Hilbert space H. It is shown that, if T or its adjoint T* is w-hyponormal, then the generalized Weyl theorem holds for f for every f ε Hole(σ(T) We also show that if T* is w-hyponormal, then the generalized a-Weyl theorem holds for f(T) for every f ε Hole(σ(T) and the B-Weyl spectrum σBW(T) and the semi-B-Fredholm spectrum σSBF+-(T) of T satisfies the spectral mapping theorem. Finally, we examine the stability of the generalized a-Weyl's theorem under commutative perturbations by finite rank operators.

Original languageEnglish
Pages (from-to)103-116
Number of pages14
JournalArabian Journal for Science and Engineering
Volume35
Issue number1 D
Publication statusPublished - May 2010

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Hyponormal Operator
Weyl's Theorem
Theorem
Spectral Mapping Theorem
Finite Rank Operators
Bounded Linear Operator
Hilbert space
Perturbation

Keywords

  • B-Fredholm theory
  • Browder's theory
  • Semi-B-Fredholm
  • Single valued extension property
  • Spectrum
  • w-hyponormal operators

ASJC Scopus subject areas

  • General

Cite this

Weyl's type theorems for algebraically w-hyponormal operators. / Rashid, M. H M; Md. Noorani, Mohd. Salmi.

In: Arabian Journal for Science and Engineering, Vol. 35, No. 1 D, 05.2010, p. 103-116.

Research output: Contribution to journalArticle

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