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~$(\delta)$. We also discuss the analytic core, decomposability and SVEP of composition operators $C_\phi$ on $l^p$ $(1\leq p<\infty)$ spaces. In particular, we prove that if $\phi$ is onto but not one-one then $C_\phi$ is not decomposable but has SVEP. Further, it is shown that if $\phi$ is one-one but not onto then $C_\phi$ does not have SVEP.