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.
Riesz Space Strongly Order Bounded Operator b-property Pre-regular Operator
Birincil Dil | İngilizce |
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Konular | Temel Matematik (Diğer) |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Erken Görünüm Tarihi | 24 Nisan 2024 |
Yayımlanma Tarihi | 30 Nisan 2024 |
Gönderilme Tarihi | 5 Ekim 2023 |
Kabul Tarihi | 22 Ocak 2024 |
Yayımlandığı Sayı | Yıl 2024 Cilt: 28 Sayı: 2 |
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