Geodesic
Rotundity In Köthe Spaces of Vector-Valued Functions
Canadian journal of mathematics, Tome 41 (1989) no. 4, pp. 659-675

Voir la notice de l'article provenant de la source Cambridge University Press

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]. 
Kamińska, A.; Turett, B. Rotundity In Köthe Spaces of Vector-Valued Functions. Canadian journal of mathematics, Tome 41 (1989) no. 4, pp. 659-675. doi: 10.4153/CJM-1989-030-2
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