On the Geometry of Cones in a Banach Space.
R. E. Gibson Library bulletin translation series,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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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
- Theoretical Mathematics