Unbounded σ-order-to-norm continuous and un-continuous operators

2019/08/08 by Mina Matin, Matin, Mina, Kazem Haghnejad Azar +3
Decision Sciences · Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.1908.03192

openalex publication_date 2019/08/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

An operator T from a vector lattice E into a normed lattice F is called unbounded σ-order-to-norm continuous whenever x_n\xrightarrowuo0 implies ‖ Tx_n‖→ 0, for each sequence (x_n)_n⊆ E. For a net (x_α)_α⊆ E, if x_α\xrightarrowun0 implies Tx_α\xrightarrowun0, then T is called an unbounded norm continuous operator. In this manuscript, we study some properties of these classes of operators and their relationships with the other classes of operators.

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