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Finite dimensional characteristics related to superreflexivity of Banach spaces

Published online by Cambridge University Press:  17 April 2009

M. I. Ostrovskii
M. I. Ostrovskii
Affiliation:
Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, United States of America, e-mail: Ostrovskii@cua.edu
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One of the important problems of the local theory of Banach Spaces can be stated in the following way. We consider a condition on finite sets in normed spaces that makes sense for a finite set any cardinality. Suppose that the condition is such that to each set satisfying it there corresponds a constant describing “how well” the set satisfies the condition.

The problem is: Suppose that a normed space X has a set of large cardinality satisfying the condition with “poor” constant. Does there exist in X a set of smaller cardinality satisfying the condition with a better constant?

In the paper this problem is studied for conditions associated with one of R.C. James's characterisations of superreflexivity.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 2 , April 2004 , pp. 289 - 295
Copyright
Copyright © Australian Mathematical Society 2004

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