# 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):

# Report Date:

## 1971-10-12

# Pagination or Media Count:

## 15.0

# Abstract:

The terminology of Krein-Krasnoselskii 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 x2 or ... or xn 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 LK bar E LK 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:

# Subject Categories:

- Theoretical Mathematics