On the relationship between three classes of operators on Riesz spaces

2015/04/29 by Liang Hong, Hong, Liang
Mathematics · #06B30 #06F30 #47B65 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B60 #Secondary 46A40

paper · pdf · doi:10.48550/arxiv.1504.08016

openalex publication_date 2015/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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