Generalised Limits for Vector Valued Sequences

Authors

  • Ajaya Kumar Singh  Department of Mathematics, Ekamra College, Bhubaneswar, Odisha, India.

DOI:

https://doi.org//10.32628/IJSRST207145

Keywords:

Banach limit, Almost convergence , Vector valued Banach limits, Vector valued Intrinsic Characterisation of Almost Convergence

Abstract

The object of the present paper is to introduce the extension of the concept of Banach limits for vector valued sequences and we prove the existence of Banach limits for vector valued sequences. Also introduced Banach spaces X,X^*,X^(**) 1-complemented in their bi duals admit vector valued Banach limits. Lastly we propose Lorentz’s vector valued intrinsic characterisation of almost convergence.

References

  1. A. Aizpuru, R. Armario, F. J. Garcia – Pacheco, F. J. Perez-Fernandez, J. Math. Anal. Appl., 379:1 (2011), 82-90.
  2. A. L. Peressini, Studia Math., 35 (1970), 111-121.
  3. E. M. Semenov, F. A. Sukochev, J. Func. Anal., 259:5 (2010), 1517-1541.
  4. G. Lorentz, Acta Math., 80 (1948), 167-190.
  5. J. Boss, Classical and Modern Methods in Summability, Oxford University Press, New York, 2000.
  6. S. Banach, Theorie des operations lineaires, Chelsea Publ., Warszawa, 1932.
  7. V. M. Kadets, B. Shumiatskiy, Matematicheskaya fizika, analiz, geometriya, 7:2 (2000), 184-195.

International Journal of Scientific Research in Science and Technology

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Published

2020-02-29

Issue

Volume 7, Issue 1, January-February-2020

Section

Research Articles

License

Copyright (c) IJSRST

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

[1]
Ajaya Kumar Singh, " Generalised Limits for Vector Valued Sequences, International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011, Volume 7, Issue 1, pp.198-202, January-February-2020. Available at doi : https://doi.org/10.32628/IJSRST207145