Some results on local spectral theory of composition operators on $l^p$ 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 $C_\phi$ on $l^p$ $(1\leq p<ınfty)$ spaces.In particular, we prove that if $\phi$ is onto but not one-onethen $C_\phi$ is not decomposable but has SVEP. Further, it isshown that if $\phi$ is one-one but not onto then $C_\phi$ doesnot have SVEP.