The Class of Demi-Strongly Order Bounded Operators

Year 2024, Volume: 28 Issue: 2, 364 - 370, 30.04.2024

Gül Sinem Keleş Birol Altın

https://doi.org/10.16984/saufenbilder.1371744

Abstract

In this paper, we introduce the class of demi-strongly order bounded operators on a Riesz space generalization of strongly order bounded operators. Let M be a Riesz space, an operator H from M into M is said to be a demi-strongly order bounded operator if for every net {u_α} in M^+ whenever 0≤u_α↑ ≤u^'',u^'' in M^(∼∼) and {u_α-H(u_α )} is order bounded in M, then {u_α} is order bounded in M. We obtain a characterization of the b-property by the term of demi-strongly order bounded operators. In addition, we study the relationship between strongly order bounded operators and demi-strongly order bounded operators. Finally, we also investigate some properties of the class of demi-strongly order bounded operators.

Keywords

Riesz Space, Strongly Order Bounded Operator, b-property, Pre-regular Operator

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