Applied and Computational Mathematics

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Topological Structure of Riesz Sequence Spaces

Received: Dec. 29, 2017    Accepted: Jan. 12, 2018    Published: Jan. 20, 2018
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Abstract

In this paper, to be the Riesz matrix is symbolized by , it is defined the spaces and where for instance and computed its duals (α-dual, β-dual and γ-dual). Furthermore, it is investigated topological structure of and determined necessary and sufficient conditions for a matrix to map , or into or .

DOI 10.11648/j.acm.20180701.14
Published in Applied and Computational Mathematics (Volume 7, Issue 1, February 2018)
Page(s) 26-30
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Topological Sequence Space, Banach Spaces, α-Dual, β-Dual

References
[1] N. P. Pahari, “Some classical sequence spaces and their topological structures, Jacem. (2015), vol 1.
[2] J. Boos, “Classical and Modern Methods in Summability”, Oxford University Press. New York, Oxford, (2000).
[3] A. Wilansky, “Summability Through Functional Analysis”, North Holland, (1984).
[4] A. Wilansky, “Functional Analysis”, Blaisdell Press, (1964).
[5] H. Kizmaz, “On Certain Sequence Spaces”, Canad. Math. Bull. Vol 24 (2) (1981), pp. 169- 176.
[6] M. Et, “On Some Difference Sequence Spaces”, Tr. J. of Math. 17 (1993), pp. 18-24.
[7] V. Pooja, “M th Difference Sequence Spaces”, IJCMS. vol 5 (2016).
[8] V. A. Khan, “Some inclusion relations between the difference sequence spaces defined by sequence of moduli”, J. Indian Math Soc. Vol 73 (2016), pp. 77-81.
[9] F.Basar, M. Kirisci, “Almost convergence and generalized difference matrix”, Comput. Math. Appl. Vol 61 (3) (2011), pp. 602-611.
[10] B. Altay, “On the space of p-summable difference sequences of order m”, Stud. Sci. Math. Hungar. Vol 43 (4) (2006), pp. 387-402.
Author Information
  • Department of Mathematics, Kahramanmaras Sutcu Imam University, Kahramanmaras, Turkey

  • Department of Primary Education, Inonu University, Malatya, Turkey

  • Department of Mathematics, Kahramanmaras Sutcu Imam University, Kahramanmaras, Turkey

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  • APA Style

    Merve Temizer Ersoy, Bilal Altay, Hasan Furkan. (2018). Topological Structure of Riesz Sequence Spaces. Applied and Computational Mathematics, 7(1), 26-30. https://doi.org/10.11648/j.acm.20180701.14

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    ACS Style

    Merve Temizer Ersoy; Bilal Altay; Hasan Furkan. Topological Structure of Riesz Sequence Spaces. Appl. Comput. Math. 2018, 7(1), 26-30. doi: 10.11648/j.acm.20180701.14

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    AMA Style

    Merve Temizer Ersoy, Bilal Altay, Hasan Furkan. Topological Structure of Riesz Sequence Spaces. Appl Comput Math. 2018;7(1):26-30. doi: 10.11648/j.acm.20180701.14

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  • @article{10.11648/j.acm.20180701.14,
      author = {Merve Temizer Ersoy and Bilal Altay and Hasan Furkan},
      title = {Topological Structure of Riesz Sequence Spaces},
      journal = {Applied and Computational Mathematics},
      volume = {7},
      number = {1},
      pages = {26-30},
      doi = {10.11648/j.acm.20180701.14},
      url = {https://doi.org/10.11648/j.acm.20180701.14},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.acm.20180701.14},
      abstract = {In this paper, to be the Riesz matrix is symbolized by , it is defined the spaces  and  where for instance  and computed its duals (α-dual, β-dual and γ-dual). Furthermore, it is investigated topological structure of  and determined necessary and sufficient conditions for a matrix  to map , or  into  or .},
     year = {2018}
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