Strongly order continuous operators on Riesz spaces

2017/12/12 by Akbar Bahramnezhad, Bahramnezhad, Akbar, Kazem Haghnejad Azar +1
Mathematics · #46B42 #47B60 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1712.04275

openalex publication_date 2017/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce two new classes of operators that we call strongly order continuous and strongly σ-order continuous operators. An operator T:E→ F between two Riesz spaces is said to be strongly order continuous (resp. strongly σ-order continuous), if x _α\xrightarrowuo0 (resp. x _n \xrightarrowuo0) in E implies Tx _α\xrightarrowo0 (resp. Tx _n \xrightarrowo0) in F. We give some conditions under which order continuity will be equivalent to strongly order continuity of operators on Riesz spaces. We show that the collection of all so-continuous linear functionals on a Riesz space E is a band of E^∼.

Citations

• Uo-convergence and its applications to Cesàro means in Banach lattices

Related

• On the relationship between three classes of operators on Riesz spaces
• Continuous Operators with Convergence in Lattice-Normed Locally Solid Riesz Spaces
• Order continuous operators on pre-Riesz spaces and embeddings
• Multiplicative order continuous operators on Riesz algebras
• Order continuity from a topological perspective