On the Geometry of Cones in a Banach Space.
Abstract
The terminology of Krein-Krasnosel'skii for Banach spaces semiordered by a cone K is used. The following assertions are proved: in order for a cone K to be normal, it is necessary and sufficient that every monotonic bounded sequence x < or = x(2) < or = ... < or = x(n) < or = ... < or = u be weakly fundamental; if a space E is weakly complete, and the cone K is normal, K is weakly regular; if a space E is weakly complete, and the cone K is normal, then K is weakly completely regular. Also given is the following definition; the cone K is called spatial if (L(K)) bar = E (L(K)) bar is the closure of the linear envelope of K). Making use of this definition some properties of the semi-group K* are established. The theorems and definitions are illustrated by examples. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 12, 1971
- Accession Number
- AD0735509
Entities
People
- I. A. Bakhtin
Organizations
- Johns Hopkins University Applied Physics Laboratory