A note on the relationship between three classes of operators on Riesz spaces-Reference-Cited by-同舟云学术

A note on the relationship between three classes of operators on Riesz spaces

Published:2019-12-01 Issue:2 Volume:57 Page:77-85
ISSN:1841-3307
Container-title:Annals of West University of Timisoara - Mathematics and Computer Science
language:en
Short-container-title:

Author:

Hong Liang¹

Affiliation:

1. John Jay 312, Department of Mathematics , Robert Morris University, 6001 University Blvd . Moon Township, PA 15108, USA

Abstract

Abstract Following several papers in the prior literature, we study the relationship between order bounded operators, topologically bounded operators and topologically continuous operators. Our main contribution is two-folded: (i) we provide a set of counterexamples to illustrate several extant results in the literature; (ii) we give conditions for the space of order bounded operators to coincide with the space of topologically bounded operators as well as conditions for these two spaces to coincide with the space of topologically continuous operators.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/awutm-2019-0016

Reference17 articles.

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4. [4] C. D. Aliprantis and O. Burkinshaw, Locally Solid Riesz Spaces with Applications to Economics, Second Edition, American Mathematical Society, Providence, Rhode Island, 2003

5. [5] N. Bourbaki, Elements of Mathematics: Topological Vector Spaces, Springer, Berlin, 1987