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Geometry of Spaces of Vector-Valued Harmonic Functions
Published online by Cambridge University Press: 20 November 2018
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.
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- Copyright © Canadian Mathematical Society 1994
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