On a generalized James constant |
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Authors: | S Dhompongsa A Kaewkhao |
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Institution: | Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand |
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Abstract: | We introduce a generalized James constant J(a,X) for a Banach space X, and prove that, if J(a,X)<(3+a)/2 for some a∈0,1], then X has uniform normal structure. The class of spaces X with J(1,X)<2 is proved to contain all u-spaces and their generalizations. For the James constant J(X) itself, we show that X has uniform normal structure provided that , improving the previous known upper bound at 3/2. Finally, we establish the stability of uniform normal structure of Banach spaces. |
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Keywords: | James constant Uniformly nonsquare space Uniform normal structure |
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