On ∗-n-paranormal operators on Banach spaces

Abstract

Let T be a ∗-n-paranormal operator on a complex Banach space X . In this paper we show that T is isoloid and if α,β are distinct eigen-values of T, then ker(T −αI)⊥ker(T −βI). Also we show that if the dual space X∗is uniformly convex and (T −αI)xk→ 0 for (xk, fk) ∈ Π(X ), then (T −αI)∗fk→ 0.