On a generalized James constant
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(...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-0141503446&partnerID=40&md5=7028f2d82a439278ccc5188d81020dfc http://cmuir.cmu.ac.th/handle/6653943832/5913 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | 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 J(X) < (1 + 5)/2, improving the previous known upper bound at 3/2. Finally, we establish the stability of uniform normal structure of Banach spaces. © 2003 Elsevier Inc. All rights reserved. |
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