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Two Aspects of Small Diameter Properties

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Operator and Matrix Theory, Function Spaces, and Applications (IWOTA 2022)

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 295))

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Abstract

In this short note, we study two different geometrical aspects of Banach spaces with small diameter properties, namely the Ball Dentable Property (BDP), Ball Huskable Property (BHP) and Ball Small Combination of slice Property (BSCSP). We show that BDP, BHP and BSCSP are separably determined properties. We also explore the stability of these properties over Köthe-Bochner spaces.

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Acknowledgements

We are grateful to the referee for going through our work meticulously and making significant comments. This work was done when the first author was visiting the Department of Pure Mathematics, University of Calcutta. She is particularly grateful to Professor Sunil Kumar Maity for his support and hospitality. The first author is also grateful to Professor Ethan Duckworkth, Chair, Department of Mathematics and Statistics, Loyola University for support towards her travel. The second author’s research is funded by the National Board for Higher Mathematics (NBHM), Department of Atomic Energy (DAE), Government of India, Ref No: 0203/11/2019-R\(\&\)D-II/9249.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Loyola University, Baltimore, MD, USA

    Sudeshna Basu

  2. Department of Mathematics, Ramakrishna Mission Vivekananda Education and Research Institute, Howrah, West Bengal, India

    Susmita Seal

Authors
  1. Sudeshna Basu
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  2. Susmita Seal
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, University of Agriculture in Kraków, Kraków, Poland

    Marek Ptak

  2. Department of Mathematics, Drexel University, Philadelphia, PA, USA

    Hugo J. Woerdeman

  3. Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

    Michał Wojtylak

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Basu, S., Seal, S. (2024). Two Aspects of Small Diameter Properties. In: Ptak, M., Woerdeman, H.J., Wojtylak, M. (eds) Operator and Matrix Theory, Function Spaces, and Applications. IWOTA 2022. Operator Theory: Advances and Applications, vol 295. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-50613-0_2

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