The Class of Demi-Strongly Order Bounded Operators
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, cilt.28, sa.2, ss.364-370, 2024 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 28 Sayı: 2
- Basım Tarihi: 2024
- Doi Numarası: 10.16984/saufenbilder.1371744
- Dergi Adı: Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Derginin Tarandığı İndeksler: Academic Search Premier, Business Source Elite, Business Source Premier, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.364-370
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Gazi Üniversitesi Adresli: Evet
Özet
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.