Isolated points of spectrum of k-quasi-*-class A operators

• Autorzy: Salah Mecheri
• Języki publikacji: EN

Abstrakty

EN

Let T be a bounded linear operator on a complex Hilbert space H. In this paper we introduce a new class, denoted 𝓚𝓠𝓐*, of operators satisfying $T^{*k}(|T²|-|T*|²)T^{k} ≥ 0$ where k is a natural number, and we prove basic structural properties of these operators. Using these results, we also show that if E is the Riesz idempotent for a non-zero isolated point μ of the spectrum of T ∈ 𝓚𝓠𝓐*, then E is self-adjoint and EH = ker(T-μ) = ker(T-μ)*. Some spectral properties are also presented.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 47B20: Subnormal operators, hyponormal operators, etc.
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 208
• Numer: 1
• Strony: 87-96

Daty

wydano

2012

Twórcy

autor

Salah Mecheri

• Department of Mathematics, College of Sciences, Taibah University, P.O. Box 20003, Al-Madinah Al Munawarah, Saudi Arabia

Identyfikatory

DOI

10.4064/sm208-1-6