The topological Riesz algebras-Reference-Cited by-同舟云学术

The topological Riesz algebras

Published:2022 Issue:7 Volume:36 Page:2325-2332
ISSN:0354-5180
Container-title:Filomat
language:en
Short-container-title:Filomat

Author:

Aydın Abdullah¹,Eroğlu Hatice²,Ilbıra Sabahattin³

Affiliation:

1. Department of Mathematics, Muş Alparslan University, Muş, Turkey

2. Department of Mathematics and Computer Science, Necmettin Erbakan University, Konya, Turkey

3. Department of Mathematics, Amasya University, Amasya, Turkey

Abstract

The multiplicative order convergence was studied and investigated on Riesz algebras. This paper deals with Riesz algebras and different topologies on them. In this paper, we investigate Riesz algebras on which we define various kinds of continuities. We give the relation between them under certain specific conditions. We show some relations among locally full, locally convex and locally solid Riesz algebras. Also, we introduce the notions of order and topological continuity of algebraic multiplications on topological Riesz algebras. Also, we extend the multiplication to quotient spaces of Riesz algebras.

Publisher

National Library of Serbia

Subject

General Mathematics

Reference40 articles.

1. C. D. Aliprantis, On the completion of Hausdorff locally solid Riesz spaces, Trans. Amer. Math. Soc. 105-125, 1974.

2. Y. A. Abramovich, G. Sirotkin, On order convergence of nets, Positivity, 9 (2005), 287-292.

3. C. D. Aliprantis, O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, second ed., Springer, Berlin, Heidelberg, New York, 2003.

4. C. D. Aliprantis, R. Tourky, Cones and duality, Graduate Studies in Mathematics, vol. 84, Amer. Math. Soc. Providence, RI, 2007.

5. C. D. Aliprantis, O. Burkinshaw, Positive operators, Academic Press, Orlando, London, 2006.