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Some degenerate binomial sequence spaces and related matrix transformations and compactness

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Abstract

The main goal of this paper is to introduce some degenerate binomial sequence spaces and to mention that these are linearly isomorphic to the spaces \(c_{0}\) and c. As well, we establish \(\alpha\)-, \(\beta\)-, \(\gamma\)-duals for these spaces and certain characterizations for some matrix classes. As an application, we deduce the characterization of certain compact operators via the Hausdorff measure of noncompactness.

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Acknowledgements

The authors thank the reviewers for their constructive comments and suggestions that have improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Akdeniz University, 07058, Antalya, Turkey

    Muhammet Cihat Dağlı & Büşra Sarıgöz Oktar

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  1. Muhammet Cihat Dağlı
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  2. Büşra Sarıgöz Oktar
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All authors contributed equally to the manuscript and read and approved the final manuscript.

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Correspondence to Muhammet Cihat Dağlı.

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Communicated by S. Ponnusamy.

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Dağlı, M.C., Sarıgöz Oktar, B. Some degenerate binomial sequence spaces and related matrix transformations and compactness. J Anal (2024). https://doi.org/10.1007/s41478-024-00731-6

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  • DOI: https://doi.org/10.1007/s41478-024-00731-6

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