Some results on local spectral theory of composition operators on lp spaces

Abstract

In this paper, we give a condition under which abounded linear operator on a complex Banach space has SingleValued Extension Property (SVEP) but does not have decompositionproperty~$(\delta )$. We also discuss the analytic core,decomposability and SVEP ofcomposition operators $C_{\varphi }$ on $l^p$ $(1\le p<ınfty)$ spaces.In particular, we prove that if $\varphi$ is onto but not one-onethen $C_{\varphi }$ is not decomposable but has SVEP. Further, it isshown that if $\varphi$ is one-one but not onto then $C_{\varphi }$ doesnot have SVEP.