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Property (k-\(\beta )\) of Musielak–Orlicz and Musielak–Orlicz–Cesàro spaces

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Abstract

In this paper, we investigate the geometric property (k-\(\beta )\) for any fixed integer \(k\ge 1\) of the space \(l_\varPhi ((E_{n}))\) generated by a Musielak–Orlicz function \(\varPhi \) and a sequence \((E_n)\) of finite dimensional spaces \(E_{n}\), \(n\in {\mathbb {N}}\), equipped with both the Luxemburg and the Amemiya norms. As a consequence, we obtain the property (k-\(\beta )\) of Musielak–Orlicz–Cesàro spaces \(ces_\varPhi \) using the approach recently considered by Saejung. Some applications to the Cesàro sequence spaces of order \(\alpha \) and Cesàro difference sequence spaces of order m are also noted.

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Acknowledgements

The authors are indebted to the anonymous referee for providing corrections and suggestions for substantial improvement of the paper. The authors wishes to record their gratitude to the Editor-in-Chief for the speedy processing of the paper.

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Authors and Affiliations

  1. Faculty of Mathematics, Indian Institute of Carpet Technology, Bhadohi, Uttar Pradesh, 221401, India

    Atanu Manna

  2. Department of Mathematics, Indian Institute of Technology, Kharagpur, West Bengal, 721302, India

    P. D. Srivastava

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  1. Atanu Manna
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  2. P. D. Srivastava
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Correspondence to Atanu Manna.

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Manna, A., Srivastava, P.D. Property (k-\(\beta )\) of Musielak–Orlicz and Musielak–Orlicz–Cesàro spaces. RACSAM 113, 471–486 (2019). https://doi.org/10.1007/s13398-017-0489-1

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