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arXiv · 2204.01991

A generalized ACK structure and the denseness of norm attaining operators

Geunsu Choi·Mingu Jung
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Abstract

Inspired by the recent work of Cascales et al., we introduce a generalized concept of ACK structure on Banach spaces. Using this property, which we call by the quasi-ACK structure, we are able to extend known universal properties on range spaces concerning the density of norm attaining operators. We provide sufficient conditions for quasi-ACK structure of spaces and results on the stability of quasi-ACK structure. As a consequence, we present new examples satisfying the (Lindenstrauss) property B$^k$, which have not been known previously. We also prove that property B$^k$ is stable under injective tensor products in certain cases. Moreover, ACK structure of some Banach spaces of vector-valued holomorphic functions is also discussed, leading to new examples of universal BPB range spaces for certain operator ideals.

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Geunsu Choi, Mingu Jung. 2022-04-05. A generalized ACK structure and the denseness of norm attaining operators. https://arxiv.org/abs/2204.01991

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