Property (m) for Bounded Linear Operators

Abstract

A bounded linear operator T acting on a Banach space  satisfies property (m) if σ (T) \ σ _ub(T) = E⁰(T), where σ_ub(T) is the upper semi-Browder spectrum of T, σ(T) is the usual spectrum of T and E⁰(T) is the set of isolated points of the spectrum σ(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.

Key words and phrases. Property (m), Property (gm); Weyl’s theorem, Weyl spectrum, Polaroid operators, Property (w).

1991 Mathematics Subject Classification. 47A10, 47A11, 47A53