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Locally uniformly rotund renorming and decompositions of Banach spaces

Published online by Cambridge University Press:  17 April 2009

V. Zizler
V. Zizler
Affiliation:
Institut fur Angewandte Mathematik der Universitat Bonn, Wegelerstr. 6, D-5300 Bonn, West Germany and Department of Mathematics, University of Alberta, Edmonton T6G 2G1, Alberta, Canada.
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A norm |·| of a Banach space x is called locally uniformly rotund if lim|xn−x| = 0 whenever xn, x ∈ X, and . It is shown that such an equivalent norm exists on every Banach space x which possesses a projectional resolution {pα} of the identify operator, for which all (pα+1−pα)X admit such norms. This applies, for example, for the dual space of a space with Fréchet differentiable norm.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 2 , April 1984 , pp. 259 - 265
Copyright
Copyright © Australian Mathematical Society 1984

References

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