New Convexity and Fixed Point Properties in Hardy and Lebesgue- Bochner Spaces
نویسندگان
چکیده
We show that for the Hardy class of functions H 1 with domain the ball or polydisc in CN , a certain type of uniform convexity property (the uniform Kadec-Klee-Huff property) holds with respect to the topology of pointwise convergence on the interior; which coincides with both the topology of uniform convergence on compacta and the weak ∗ topology on bounded subsets of H 1. Also, we show that if a Banach space X has a uniform Kadec-Klee-Huff property, then the Lebesgue-Bochner space L p(μ,X) 1 ≤ p < ∞ must have a related uniform Kadec-Klee-Huff property. Consequently, by known results, the above spaces have normal structure properties and fixed point properties for non-expansive mappings.
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