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Uniform asymptotic smoothness of norms

Published online by Cambridge University Press:  17 April 2009

T. Lewis ,
J. Whitfield  and
V. Zizler
T. Lewis
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
J. Whitfield
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, P7B 5E1, Canada.
V. Zizler
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada.
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Abstract

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We study a notion of smoothness of a norm on a Banach space X which generalizes the notion of uniform differentiability and is formulated in terms of unicity of Hahn Banach extensions of functionals on block subspaces of a fixed Schauder basis S in X. Variants of this notion have already been used in estimating moduli of convexity in some spaces or in fixed point theory. We show that the notion can also be used in studying the convergence of expansions coefficient of elements of X* along the dual basis S*.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 457 - 470
Copyright
Copyright © Australian Mathematical Society 1986

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