Characterizations of universal finite representability and b-convexity of Banach spaces via ball coverings

Authors
Citation
Zhang, Wen, Characterizations of universal finite representability and b-convexity of Banach spaces via ball coverings, Acta mathematica Sinica. English series (Print) , 28(7), 2012, pp. 1369-1374
ISSN journal
14398516
Volume
28
Issue
7
Year of publication
2012
Pages
1369 - 1374
Database
ACNP
SICI code
Abstract
By a ball-covering B of a Banach space X, wemean that B is a collection of open (or closed) balls off the origin whose union contains the unit sphere of X; and X is said to have the ball-covering property provided it admits a ball-covering of countably many balls. This paper shows that universal finite representability and B-convexity of X can be characterized by properties of ball-coverings of its finite dimensional subspaces.