
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