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Rotundity In Köthe Spaces of Vector-Valued Functions

Published online by Cambridge University Press:  20 November 2018

A. Kamińska  and
B. Turett
A. Kamińska
Affiliation:
A. Mickiewicz University, Poznań, Poland
B. Turett
Affiliation:
Oakland University, Rochester, Michigan
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In this paper, Köthe spaces of vector-valued functions are considered. These spaces, which are generalizations of both the Lebesgue-Bochner and Orlicz-Bochner spaces, have been studied by several people (e.g., see [1], [8]). Perhaps the earliest paper concerning the rotundity of such Köthe space is due to I. Halperin [8]. In his paper, Halperin proved that the function spaces E(X) is uniformly rotund exactly when both the Köthe space E and the Banach space X are uniformly rotund; this generalized the analogous result, due to M. M. Day [4], concerning Lebesgue-Bochner spaces. In [20], M. Smith and B. Turett showed that many properties akin to uniform rotundity lift from X to the Lebesgue-Bochner space LP(X) when 1 < p < ∞. A survey of rotundity notions in Lebesgue-Bochner function and sequence spaces can be found in [19].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 4 , 01 August 1989 , pp. 659 - 675
Copyright
Copyright © Canadian Mathematical Society 1989

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