Abstract. The property $(w)$ is a variant of Weyl's theorem, for a bounded operator $T$ acting on a Banach space. In this note we consider the preservation of property $(w)$ under compact, or Riesz, or algebraic perturbations commuting with $T$. We shall also give some perturbation results on the generalized property $(gw)$.

AMS Subject Classification (1991): 47A10, 47A11, 47A53, 47A55

Keyword(s): property $(w)$, SVEP, Riesz operators

Received October 27, 2008, and in revised form August 14, 2009. (Registered under 58/2010.)