Topological Structure of Riesz Sequence Spaces
Applied and Computational Mathematics
Volume 7, Issue 1, February 2018, Pages: 26-30
Received: Dec. 29, 2017;
Accepted: Jan. 12, 2018;
Published: Jan. 20, 2018
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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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In this paper, to be the Riesz matrix is symbolized by
, it is defined the spaces
where for instance
and computed its duals (α
-dual and γ
-dual). Furthermore, it is investigated topological structure of
and determined necessary and sufficient conditions for a matrix
Topological Sequence Space, Banach Spaces, α-Dual, β-Dual
To cite this article
Merve Temizer Ersoy,
Topological Structure of Riesz Sequence Spaces, Applied and Computational Mathematics.
Vol. 7, No. 1,
2018, pp. 26-30.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
N. P. Pahari, “Some classical sequence spaces and their topological structures, Jacem. (2015), vol 1.
J. Boos, “Classical and Modern Methods in Summability”, Oxford University Press. New York, Oxford, (2000).
A. Wilansky, “Summability Through Functional Analysis”, North Holland, (1984).
A. Wilansky, “Functional Analysis”, Blaisdell Press, (1964).
H. Kizmaz, “On Certain Sequence Spaces”, Canad. Math. Bull. Vol 24 (2) (1981), pp. 169- 176.
M. Et, “On Some Difference Sequence Spaces”, Tr. J. of Math. 17 (1993), pp. 18-24.
V. Pooja, “M th Difference Sequence Spaces”, IJCMS. vol 5 (2016).
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.
F.Basar, M. Kirisci, “Almost convergence and generalized difference matrix”, Comput. Math. Appl. Vol 61 (3) (2011), pp. 602-611.
B. Altay, “On the space of p-summable difference sequences of order m”, Stud. Sci. Math. Hungar. Vol 43 (4) (2006), pp. 387-402.