Characterization of collectively compact sets of linear operators

Abstract

The basic results in this paper show that each collectively compact set of linear operators can be viewed as an equicontinuous collection followed by a single compact operator. This observation not only gives insight into the character of collectively compact sets of linear operators, but also yields easier proofs of many of the results obtained by earlier workers in the field. I* Factorizations of collectively compact operators* A fairly complete treatment, with applications, of collectively compact sets of linear operators is given in the recent book [1] by Anselone. Collectively compact sets of linear operators on normed linear spaces were originally studied by Anselone and Moore [2] in connection with approximate solutions of integral and operator equations. The general properties of such sets of operators, again in normed linear spaces, were studied by Anselone and Palmer in [3] and [4]. Collectively compact sets of linear operators were studied in the more general setting of linear topological spaces by DePree and Higgins [5]. In the current work new characterizations are given for collectively compact sets of operators on a linear topological space.