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.
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)
