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On the duality of the symmetric strong diameter 2 property in Lipschitz 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 characterise the weak\(^*\) symmetric strong diameter 2 property in Lipschitz function spaces by a property of its predual, the Lipschitz-free space. We call this new property decomposable octahedrality and study its duality with the symmetric strong diameter 2 property in general. For a Banach space to be decomposably octahedral it is sufficient that its dual space has the weak\(^*\) symmetric strong diameter 2 property. Whether it is also a necessary condition remains open.

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Acknowledgements

The paper is a part of a Ph.D. thesis which is being prepared by the author at University of Tartu under the supervision of Rainis Haller and Märt Põldvere. The author is grateful to his supervisors for their valuable help. This work was supported by the Estonian Research Council grant (PRG877). The author wishes to thank the anonymous referees for helpful suggestions and remarks.

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  1. Tartu Ulikool Matemaatika ja statistika instituut Tartu, Tartu, Estonia

    Andre Ostrak

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  1. Andre Ostrak
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Correspondence to Andre Ostrak.

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Ostrak, A. On the duality of the symmetric strong diameter 2 property in Lipschitz spaces. RACSAM 115, 78 (2021). https://doi.org/10.1007/s13398-021-01018-2

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