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Almost squareness and strong diameter two property in tensor product spaces

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We study almost squareness and the strong diameter two property in the setting of projective (symmetric) tensor product of Banach spaces. We prove that almost squareness is stable by taking projective tensor products, providing non-trivial examples of ASQ projective tensor products of Banach spaces. Furthermore, we give sufficient conditions for a projective symmetric tensor product to have the strong diameter two property. This extend most of the previously known results and provide new examples of projective symmetric tensor product spaces with the strong diameter two property.

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Acknowledgements

The author thanks the anonymous referees for their valuable suggestions which have improved the exposition of the paper.

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  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Abraham Rueda Zoca

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  1. Abraham Rueda Zoca
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Correspondence to Abraham Rueda Zoca.

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The research of Abraham Rueda Zoca was supported by Vicerrectorado de Investigación y Transferencia de la Universidad de Granada in the program “Contratos puente”, by MICINN (Spain) Grant PGC2018-093794-B-I00 (MCIU, AEI, FEDER, UE), by Junta de Andalucía Grant A-FQM-484-UGR18 and by Junta de Andalucía Grant FQM-0185.

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Rueda Zoca, A. Almost squareness and strong diameter two property in tensor product spaces. RACSAM 114, 84 (2020). https://doi.org/10.1007/s13398-020-00816-4

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