PROPERTY (m) FOR BOUNDED LINEAR OPERATORS

A bounded linear operator T acting on a Banach space satisfies property (m) if ᵟ(T) n ᵟub(T) = E^0(T); where ᵟub(T) is the upper semi-Browder spectrum of T, ᵟ(T) is the usual spectrum of T and E0(T) is the set of isolated points of the spectrum ᵟ(T) of T which are eigenvalues of finite multiplicity. In this paper we introduce and study new properties (m); and (gm), which are related to Weyl type theorems. These properties are also studied in the framework of polaroid operators.