关于洪福猜想(英文) |
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引用本文: | 张文耀
,俞鑫泰.关于洪福猜想(英文)[J].华东师范大学学报(自然科学版),1984(1). |
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作者姓名: | 张文耀 俞鑫泰 |
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摘 要: | In1],R.Huff introduced the concept of nearly uniformly convex Banach space.A Banach space X is said to be nearly uniformly convex(NUC) if for any ε>0,there exists δ<1,such that whenever {X_n}??X,||X_n||≤1,sep(X_n)=inf{||x_n-x_m||·m≠n}>ε,then there exist a_i≥0,i=1,…,n,sum for i=1 to n (a_i=1),and ||sum for i=1 to n (a_ix_i)||≤δ. R.Huff conjectured that NUC Banach space has the Banach Saks property(A Banach space X has the Bana ch-Sakseproperty(BSP) whenever every bounded sequence in X has a subsequence whose arithmetic means converge in norm.In this note,we give a negative answer to this conjecture. First we give a sufficient condition of NUC space.
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