On the spectra of some non-normal operators

M. H M Rashid, Mohd. Salmi Md. Noorani, A. S. Saari

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this paper, we prove the following: (1) If T is invertible ω-hyponormal completely non-normal, then the point spectrum is empty. (2) If T1 and T2 are injective ω-hyponormal and if T and S are quasisimilar, then they have the same spectra and essential spectra. (3) If T is (p, k)-quasihyponormal operator, then σjp(T)-{0} = σap(T)-{0}. (4) If T*, S ∈ B(H) are injective (p, k)-quasihyponormal operator, and if XT =SX, where X ∈B(H) is an invertible, then there exists a unitary operator U such that UT = SU and hence T and S are normal operators.

Original languageEnglish
Pages (from-to)135-143
Number of pages9
JournalBulletin of the Malaysian Mathematical Sciences Society
Volume31
Issue number2
Publication statusPublished - 2008

Fingerprint

Injective
Invertible
Normal Operator
Unitary Operator
Point Spectrum
Essential Spectrum
Operator

Keywords

  • ω-hyponormal
  • (p,k)-quasihyponormal
  • Class A
  • Quasisimilarity
  • Weyl's theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the spectra of some non-normal operators. / Rashid, M. H M; Md. Noorani, Mohd. Salmi; Saari, A. S.

In: Bulletin of the Malaysian Mathematical Sciences Society, Vol. 31, No. 2, 2008, p. 135-143.

Research output: Contribution to journalArticle

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