Accession Number : AD0660502

Title :   COLLECTIVELY COMPACT AND TOTALLY BOUNDED SETS OF LINEAR OPERATORS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Anselone,P. M.

Report Date : JUL 1967

Pagination or Media Count : 21

Abstract : A set Kappa of linear operators on a normed linear space X into a normed linear space Y is collectively compact if the set (Kx : K epsilon Kappa, Norm x = or < 1) has compact closure. It is proved that if Kappa and Kappa star = (K star : K epsilon Kappa) are collectively compact and dim KX = or < n for all K epsilon Kappa (n = 1, 2, ...), then Kappa is totally bounded. (Author)

Descriptors :   (*FUNCTIONAL ANALYSIS, *OPERATORS(MATHEMATICS)), SET THEORY, TOPOLOGY, HILBERT SPACE, BANACH SPACE, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE