Vol. 26, No. 3, 1968

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
Author Index
To Appear
ISSN: 0030-8730
Normal structure in Banach spaces

Lawrence Peter Belluce, William A. Kirk and Eugene Francis Steiner

Vol. 26 (1968), No. 3, 433–440

A bounded convex subset K of a Banach space B has normal structure if for each convex subset H of K which contains more than one point there is a point x in H which is not a diametral point of H. The concept of normal structure (introduced by Brodskii and Milman) and a strengthening of this concept called complete normal structure have been of fundamental importance in some recent investigations concerned with determining conditions on weakly compact K under which the members of any commutative family 𝒯 of nonexpansive mappings of K into itself have a common fixed-point. A more thorough study of these concepts is initiated in the present paper. The theorems obtained primarily concern product spaces composed of spaces which possess normal structure.

Mathematical Subject Classification
Primary: 46.10
Received: 11 October 1966
Published: 1 September 1968
Lawrence Peter Belluce
William A. Kirk
Eugene Francis Steiner