Accession Number : AD0735509

Title :   On the Geometry of Cones in a Banach Space.

Descriptive Note : R. E. Gibson Library bulletin translation series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Bakhtin,I. A.

Report Date : 12 OCT 1971

Pagination or Media Count : 15

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)

Descriptors :   (*BANACH SPACE, THEOREMS), SEQUENCES, SET THEORY, CONVERGENCE, CONICAL BODIES, USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE