Abstract: Given H a Hilbert space and B(H) the algebra of
bounded linear operator in H, let δAB denote the generalized
derivation defined by A and B. The main objective of this article
is to study Weyl type theorems for generalized derivation for (A,B)
satisfying a couple of Fuglede.
Abstract: A Banach space operator T obeys property (gm) if the
isolated points of the spectrum σ(T) of T which are eigenvalues
are exactly those points λ of the spectrum for which T − λI is
a left Drazin invertible. In this article, we study the stability of
property (gm), for a bounded operator acting on a Banach space,
under perturbation by finite rank operators, by nilpotent operators,
by quasi-nilpotent operators, or more generally by algebraic operators
commuting with T.