Recent perturbation results for exponentially dichotomous operators are generalized, in part by replacing compactness conditions on the perturbation by resolvent compactness. Both additive and multiplicative perturbations are considered. Mathematics Subject Classification (2000). Primary 47D06; Secondary 47A55.

The concepts of β-compactness and βclosed spaces in the fuzzy setting are defined and investigated. Fuzzy filterbases are used to characterize these concepts. A comparison between these types and some different forms of compactness in fuzzy topology is established.