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Uniform Kadec–Klee–Huff properties of vector-valued Hardy spaces

Published online by Cambridge University Press:  24 October 2008

P. N. Dowling  and
C. J. Lennard
P. N. Dowling
Affiliation:
Miami University, Oxford, Ohio 4506, USA
C. J. Lennard
Affiliation:
University of Pittsburgh, Pittsburgh, PA 15260, USA
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Abstract

In [8] Partington showed that a Banach space X is uniformly convex if and only if Lp([0, 1], X) has the uniform Kadec–Klee–Huff property with respect to the weak topology (UKKH (weak)), where 1 < p < ∞. In this note we will characterize the Banach spaces X such that HP(D, X) has UKKH (weak), where 1 ≤ p < ∞. Similar results for UKKH (weak*) are also obtained. These results (and proofs) are quite different from Partington's result (and proof).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 114 , Issue 1 , July 1993 , pp. 25 - 30
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

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