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arXiv · 2012.09492

Stability of diametral diameter two properties

Johann Langemets·Katriin Pirk
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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 K\"othe-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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Johann Langemets, Katriin Pirk. 2020-12-17. Stability of diametral diameter two properties. https://arxiv.org/abs/2012.09492

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