The Class of Demi-Strongly Order Bounded Operators

Authors : Gül Sinem Keleş, Birol Altın

Pages : 364-370

Doi:10.16984/saufenbilder.1371744

View : 43 | Download : 96

Publication Date : 2024-04-30

Article Type : Research Paper

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