Stability of diametral diameter two properties

2020/12/17 by Langemets, Johann, Pirk, Katriin
#46B04 #46B20 #46B22 #46B42 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2012.09492

Abstract

We prove that the diametral diameter two properties are inherited by F-ideals (e.g., M-ideals). On the other hand, these properties are lifted from an M-ideal to the superspace under strong geometric assumptions. We also show that all of the diametral diameter two properties are stable under the formation of corresponding Köthe-Bochner spaces (e.g., L_p-Bochner spaces). Finally, we investigate when the projective tensor product of two Banach spaces has some diametral diameter two property.

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