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On Fragments on Lattice Normed Vector Lattices

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Abstract

In the present paper, we investigate (bo)-fragments in lattice normed spaces. After showing that every (bo)-fragment of a positive element is a fragment in the case of lattice normed vector lattices, we prove that the collection of all (bo)-fragments of a positive element forms an order complete Boolean algebra. Several examples and detailed discussions of various cases are presented.

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Acknowledgements

We would like to thank the referee for her/his valuable suggestions. This work is partially supported by the Scientific Research Projects Coordination Unit of Hacettepe University, Project ID: FBA-2021-19488.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Hacettepe University, 06800, Ankara, Turkey

    Sezer Bolat & Nazife Erkurşun-Özcan

  2. Department of Mathematics, Faculty of Arts and Sciences, TED University, 06420, Ankara, Turkey

    Niyazi Anıl Gezer

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  1. Sezer Bolat
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  2. Nazife Erkurşun-Özcan
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  3. Niyazi Anıl Gezer
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Correspondence to Sezer Bolat.

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Bolat, S., Erkurşun-Özcan, N. & Gezer, N.A. On Fragments on Lattice Normed Vector Lattices. Results Math 78, 245 (2023). https://doi.org/10.1007/s00025-023-02017-y

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  • DOI: https://doi.org/10.1007/s00025-023-02017-y

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