TY - JOUR
T1 - The Class of Demi-Strongly Order Bounded Operators
AU - Altın, Birol
AU - Keleş, Gül Sinem
PY - 2024
DA - April
Y2 - 2024
DO - 10.16984/saufenbilder.1371744
JF - Sakarya University Journal of Science
JO - SAUJS
PB - Sakarya University
WT - DergiPark
SN - 2147-835X
SP - 364
EP - 370
VL - 28
IS - 2
LA - en
AB - 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.
KW - Riesz Space
KW - Strongly Order Bounded Operator
KW - b-property
KW - Pre-regular Operator
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UR - https://doi.org/10.16984/saufenbilder.1371744
L1 - https://dergipark.org.tr/en/download/article-file/3456529
ER -