Topological Structure of Riesz Sequence Spaces

Merve Temizer Ersoy; Bilal Altay; Hasan Furkan

doi:doi:10.11648/j.acm.20180701.14

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Topological Structure of Riesz Sequence Spaces

Merve Temizer Ersoy, Bilal Altay, Hasan Furkan

Published in Applied and Computational Mathematics (Volume 7, Issue 1)

Received: 29 December 2017 Accepted: 12 January 2018 Published: 20 January 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 .

Published in	Applied and Computational Mathematics (Volume 7, Issue 1)
DOI	10.11648/j.acm.20180701.14
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), 2018. 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.

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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Topological Structure of Riesz Sequence Spaces
AU  - Merve Temizer Ersoy
AU  - Bilal Altay
AU  - Hasan Furkan
Y1  - 2018/01/20
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DO  - 10.11648/j.acm.20180701.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 26
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PB  - Science Publishing Group
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AB  - 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 .
VL  - 7
IS  - 1
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Author Information

Merve Temizer Ersoy

Department of Mathematics, Kahramanmaras Sutcu Imam University, Kahramanmaras, Turkey
Bilal Altay

Department of Primary Education, Inonu University, Malatya, Turkey
Hasan Furkan

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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Topological Structure of Riesz Sequence Spaces
AU  - Merve Temizer Ersoy
AU  - Bilal Altay
AU  - Hasan Furkan
Y1  - 2018/01/20
PY  - 2018
N1  - https://doi.org/10.11648/j.acm.20180701.14
DO  - 10.11648/j.acm.20180701.14
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 26
EP  - 30
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20180701.14
AB  - 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 .
VL  - 7
IS  - 1
ER  -

Copy | Download