Summary
Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm. We study in this paper Banach-Saks operators defined on C(K, E) spaces. We characterize these operators for a large class of compacts K (the scattered ones), or for a large class of Banach spaces E (the superreflexive ones). We also show by some examples that our theorems can not be extended directly.
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Partially supported by C.A.I.C.Y.T. grant 0338-84. The author wishes to thank Professor F.Bombal for his encouragement.
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Nú¯nez, C. Banach-Saks operators on spaces of continuous functions. Annali di Matematica 161, 43–56 (1992). https://doi.org/10.1007/BF01759631
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DOI: https://doi.org/10.1007/BF01759631