COLLECTIVELY COMPACT AND TOTALLY BOUNDED SETS OF LINEAR OPERATORS.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1967
- Accession Number
- AD0660502
Entities
People
- P. M. Anselone
Organizations
- University of Wisconsin–Madison