Research
On operators satisfying an inequality
Department of Mathematics, College of Science, Taibah University, P.O. Box 30002, Al-Madinah-Al-Munawarah, Saudi Arabia
Journal of Inequalities and Applications 2012, 2012:244 doi:10.1186/1029-242X-2012-244
Published: 24 October 2012Abstract
An operator T is said to be k-quasi-∗-class A if 
, where k is a natural number. Let 
denote either the generalized derivation 
or the elementary operator 
, where 
and 
are the left and right multiplication operators defined on 
by 
and 
respectively. This article concerns some spectral properties of k-quasi-∗-class A operators in a Hilbert space, as the property of being hereditarily polaroid. We
also establish Weyl-type theorems for T and 
, where T is a k-quasi-∗-class A operator and A, 
are also k-quasi-∗-class A operators.
MSC: 47B47, 47A30, 47B20, 47B10.
