Volume 7, Issue 1, February 2018, Page: 26-30
Topological Structure of Riesz Sequence Spaces
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
Received: Dec. 29, 2017;       Accepted: Jan. 12, 2018;       Published: Jan. 20, 2018
DOI: 10.11648/j.acm.20180701.14      View  1393      Downloads  85
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 .
Keywords
Topological Sequence Space, Banach Spaces, α-Dual, β-Dual
To cite this article
Merve Temizer Ersoy, Bilal Altay, Hasan Furkan, Topological Structure of Riesz Sequence Spaces, Applied and Computational Mathematics. Vol. 7, No. 1, 2018, pp. 26-30. doi: 10.11648/j.acm.20180701.14
Copyright
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.
Reference
[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.
Browse journals by subject