Weyl's type theorems for algebraically (p, k)-quasihyponormal operators

Mohammad Hussein Mohammad Rashid, Mohd. Salmi Md. Noorani

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

For a bounded linear operator T we prove the following assertions: (a) If T is algebraically (p, k)-quasihyponormal, then T is a-isoloid, polaroid, reguloid and a-polaroid. (b) If T* is algebraically (p, k)-quasihyponormal, then a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)), where Hol(σ(T)) is the space of all functions that analytic in an open neighborhoods of σ(T) of T. (c) If T* is algebraically (p, k)-quasihyponormal, then generalized a-Weyl's theorem holds for f(T) for every f ∈ Hol(σ(T)). (d) If T is a (p, k)-quasihyponormal operator, then the spectral mapping theorem holds for semi-B-essential approximate point spectrum σ SBF - +(T), and for left Drazin spectrum σ lD(T) for every f ∈ Hol(σ(T)).

Original languageEnglish
Pages (from-to)77-95
Number of pages19
JournalCommunications of the Korean Mathematical Society
Volume27
Issue number1
DOIs
Publication statusPublished - 2012

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Weyl's Theorem
Spectral Mapping Theorem
Point Spectrum
Bounded Linear Operator
Operator
Assertion
Theorem
Analytic function

Keywords

  • (p, k)-quasihyponormal
  • Browder's theory
  • Fredholm theory
  • Single valued extension property
  • Spectrum

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Weyl's type theorems for algebraically (p, k)-quasihyponormal operators. / Rashid, Mohammad Hussein Mohammad; Md. Noorani, Mohd. Salmi.

In: Communications of the Korean Mathematical Society, Vol. 27, No. 1, 2012, p. 77-95.

Research output: Contribution to journalArticle

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