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

Abstract

In this paper, we give a condition under which a bounded linear operator on a complex Banach space has Single Valued Extension Property (SVEP) but does not have decomposition property (±). We also discuss the analytic core, decomposability and SVEP of composition operators CÁ on lp (1 · p < 1) spaces. In particular, we prove that if Á is onto but not one-one then CÁ is not decomposable but has SVEP. Further, it is shown that if Á is one-one but not onto then CÁ does not have SVEP.