(s)-nuclear sets and operators

Abstract

The purpose of this paper is to demonstrate considerable similarities in the behaviour of compact and O)-nuclear operators. More precisely, we obtain for (s)-nuclear operators results resembling previously known properties of compact operators; sometimes a word for word translation of a "compact theorem" holds for (s)-nudear operators. However, we wish to emphasize that different methods for the proofs are now needed. For example, the often applied Ascoli-Arzela theorem does not have a (s)-nuclear counterpart (see §5).