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《Journal of Anhui Normal University(Natural Science)》 1989-01
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A Generalization of Taylor—Fougel Theorem

Nan Chaoxun(Department of Mathematics)  
Let X be a Banach space and M a subspace of X. For every f∈M~*, set E_M(f)={g∈X~*: ‖g‖=‖f‖_M and g(x)=f(x) for x∈M}. The subspace M is said to have the property (U_k) if for every f∈M~*, the dimE_M(f) satisfies the inequality dimE_M(f)≤k, where k is a positive integral. In this paper, the following results are obtained. Theorem 1. Every subspace of a Banach space X has property (U_k) if and only if X~* is k-strictly convex. This is a generalization of Taylor-Fougel theorem. Theorem 2. If X is k-UR space, then every subspace of X~* has property
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