On ?-n-paranormal operators on Banach spaces

摘要

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.