On The Radius Problems Of Ball-coverings Of N-dimensional Spaces

Let X be a Banach Space,Sx be the unit sphere of X.By a ball-covering B = {B_?}??A of Sx,we always mean each B in B is a closed ball off the origin and SX(?)??? B_?.We say that a ball covering B of SX has radius r if r = r(B)= sup {s:B(x,s)?B},where B(x,s)is the closed ball centered at x with radius s.The minimum radius of ball-coverings with cardinality m of SRn is defined as rmin = min{r(B):SRn(?)?B,B#=m}.In 2008,Guochen Lin and Xisheng Shen gave a formula of the minimum radius of ball-coverings with cardinality m of Sl2n.In particular,they showed rmin =(?)/2 and rmin=n/2,respectively,as m = 2n and m = n + 1,respectively.In this paper,we consider the radius problems of ball-coverings with cardinality 2n of Slpn(p?2).As a result,we show the possible range of r when Slpn(?)Ui=1nB(±rei,r)(r>0),where ei denotes the standard unit vectors of l_p~n.