An elementary operator and generalized Weyl’s theorem
College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan, 453007, China
Journal of Inequalities and Applications 2012, 2012:243 doi:10.1186/1029-242X-2012-243Published: 24 October 2012
A Hilbert space operator T belongs to class A if . Let denote either or , where and denote the generalized derivation and the elementary operator on a Banach space defined by and respectively. If A and are class A operators, we show that is polaroid and generalized Weyl’s theorem holds for , generalized a-Weyl’s theorem holds for for every and f is not constant on each connected component of the open set U containing , where denotes the set of all analytic functions in a neighborhood of .
MSC: 47B20, 47A63.