The W-convexity and normal structure in banach spaces |
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Authors: | J. Gao |
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Affiliation: | Department of Mathematics, Community College of Philadelphia Philadelphia, PA 19130-3991, U.S.A. |
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Abstract: | Let X be a Banach space, S(X) - x ε X : #x02016; = 1 be the unit sphere of X.The parameter, modulus of W*-convexity, W*(ε) = inf <(x − y)/2, fx> : x, y S(X), x − y ≥ ε, fx Δx , where 0 ≤ ε ≤ 2 and Δx S(X*) be the set of norm 1 supporting functionals of S(X) at x, is investigated_ The relationship among uniform nonsquareness, uniform normal structure and the parameter W*(ε) are studied, and a known result is improved. The main result is that for a Banach space X, if there is ε, where 0 < ε < 1/2, such that W*(1 + ε) > ε/2 where W*(1 + ε) = lim→ε W* (1 + ), then X has normal structure. |
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Keywords: | Modulus of convexity Modulus of W*-convexity Normal structure Uniformly nonsquarespace Uniform normal structure |
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