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Compact operators on spaces of binomial fractional difference sequences

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Abstract

In this paper, we intend to form certain estimates and identities for the norm of matrix operator from \(\ell _{r}\)-type binomial fractional difference sequence space into \(c, c_{0}, \ell _{\infty }\) and \(\ell _{1}\) sequences spaces. We obtain the necessary and sufficient conditions for some classes of compact operators on \(\ell _{r}\)-type binomial fractional difference sequence space \((1 \le r < \infty )\) by employing the Hausdorff measure of non-compactness.

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Acknowledgements

The author (K. Raj) thanks the Council of Scientific and Industrial Research (CSIR), India for support under Grant No. 25(0288)/18/EMR-II, dated 24/05/2018. Research of the author (M. Mursaleen) was supported by SERB Core Research Grant, DST, New Delhi, under Grant No. EMR/2017/000340.

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Authors and Affiliations

  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, J & K, 182320, India

    Anu Choudhary & Kuldip Raj

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India

    M. Mursaleen

  3. Department of Medical Research, China Medical University Hospital, China Medical University (Taiwan), Taichung, Taiwan

    M. Mursaleen

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  1. Anu Choudhary
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  2. Kuldip Raj
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  3. M. Mursaleen
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The authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.

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Correspondence to M. Mursaleen.

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Choudhary, A., Raj, K. & Mursaleen, M. Compact operators on spaces of binomial fractional difference sequences. Math Sci 16, 79–85 (2022). https://doi.org/10.1007/s40096-021-00396-3

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