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Geometry of Spaces of Vector-Valued Harmonic Functions

Published online by Cambridge University Press:  20 November 2018

Patrick N. Dowling ,
Zhibao Hu  and
Mark A. Smith
Patrick N. Dowling
Affiliation:
Department of Mathematics and Statistics Miami University Oxford, Ohio 45056 U.S.A.
Zhibao Hu
Affiliation:
Department of Mathematics and Statistics Miami University Oxford, Ohio 45056 U.S.A.
Mark A. Smith
Affiliation:
Department of Mathematics and Statistics Miami University Oxford, Ohio 45056 U.S.A.
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Abstract

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It is shown that the space hp(D,X) has the Kadec-Klee property with respect to pointwise norm convergence in the Banach space X if and only if X has the Radon-Nikodym property and every point of the unit sphere of X is a denting point of the unit ball of X. In addition, it is shown that hp(D,X) is locally uniformly rotund if and only if X is locally uniformly rotund and has the Radon-Nikodym property.

Keywords

46B2046E40vector-valued harmonic functionsKadec-Klee propertieslocal uniform rotundity
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 2 , 01 April 1994 , pp. 274 - 283
Copyright
Copyright © Canadian Mathematical Society 1994

References

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