一些 Banach空间的非正方形系数(英文)

Non-square Coefficient for Some Banach Spaces

给出了一些 Banach空间的非正方形系数 ,证明了 :如果 X是满足 dim X≥ 2的严格凸空间 ,则 N S(l1 (X) ) <2 ,NS(l∞ (X) ) <2 ;对任意的 Banach空间 X,有 NS(l1 (X) ) =1 ,N S(l∞ (X) ) =1 ,及 N S(lp (X) )≤ min{2 1 / p ,2 1 / q}.特别 ,当 X是一个 Hilbert空间时 ,N S(l2 (X ) )

The non square coefficient for some Banach spaces is computed. It is shown that if X is a strictly convex space satisfying dim X ≥2, then NS(l 1(X))<2, NS(l ∞(X))<2 . For any Banach space X, NS(l 1(X))=1, NS(l ∞(X))=1, and NS(l p(X))≤ min {2 1/p , 2 1/q } , in particular, when X is a Hilbert space, NS(l 2(X))=2.