Research
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-2012-243
Published: 24 October 2012Abstract
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.
