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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2014
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th-cmuir.6653943832-59132014-08-30T03:23:36Z On a generalized James constant Dhompongsa S. Kaewkhao A. Tasena S. 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. 2014-08-30T03:23:36Z 2014-08-30T03:23:36Z 2003 Article 0022247X 10.1016/S0022-247X(03)00408-6 http://www.scopus.com/inward/record.url?eid=2-s2.0-0141503446&partnerID=40&md5=7028f2d82a439278ccc5188d81020dfc http://cmuir.cmu.ac.th/handle/6653943832/5913 English |
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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. |
| format |
Article |
| author |
Dhompongsa S. Kaewkhao A. Tasena S. |
| spellingShingle |
Dhompongsa S. Kaewkhao A. Tasena S. On a generalized James constant |
| author_facet |
Dhompongsa S. Kaewkhao A. Tasena S. |
| author_sort |
Dhompongsa S. |
| title |
On a generalized James constant |
| title_short |
On a generalized James constant |
| title_full |
On a generalized James constant |
| title_fullStr |
On a generalized James constant |
| title_full_unstemmed |
On a generalized James constant |
| title_sort |
on a generalized james constant |
| publishDate |
2014 |
| url |
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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1681420515200204800 |