Characterizations of Universal Finite Representability and B-convexity of Banach Spaces via Ball Coverings  

作　　者：Wen ZHANG 

机构地区：[1]School of Mathematical Sciences,Xiamen University

出　　处：《Acta Mathematica Sinica,English Series》2012年第7期1369-1374,共6页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10771175, 10801111 and 11101340);the Natural Science Foundation of Fujian Province (Grant No. 2010J05012) ;the Fundamental Research Funds for the Central Universities (Grant Nos. 2010121001 and 2011121039)

摘　　要：By a ball-covering B of a Banach space X, we mean 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.By a ball-covering B of a Banach space X, we mean 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.

关 键 词：BALL-COVERING finite representability CONVEXITY universal space Banach space 

分 类 号：O177.2[理学—数学] O189.11[理学—基础数学]