Order-to-topology continuous operators

2019/05/25 by Azar, Kazem Haghnejad · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.10577

Abstract

An operator T from vector lattice E into vector topology (F,τ) is said to be order-to-topology continuous whenever x_α\xrightarrowo0 implies Tx_α\xrightarrowτ0 for each (x_α)_α⊂ E. The collection of all order-to-topology continuous operators will be denoted by L_oτ(E,F). In this paper, we will study some properties of this new classification of operators. We will investigate the relationships between order-to-topology continuous operators and others classes of operators such as order continuous, order weakly compact and b-weakly compact operators.

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