1. bookVolume 57 (2019): Issue 2 (December 2019)
Journal Details
License
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Journal
First Published
22 Nov 2012
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2 times per year
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English
access type Open Access

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

Published Online: 21 Dec 2020
Page range: 77 - 85
Journal Details
License
Format
Journal
First Published
22 Nov 2012
Publication timeframe
2 times per year
Languages
English
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.

Keywords

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