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arXiv · 1908.03192

Unbounded $\sigma$-order-to-norm continuous and $un$-continuous operators

Mina Matin·Kazem Haghnejad Azar·Razi Alavizadeh
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Abstract

An operator $T $ from a vector lattice $E$ into a normed lattice $F$ is called unbounded $\sigma$-order-to-norm continuous whenever $x_{n}\xrightarrow{uo}0$ implies $\| Tx_{n}\|\rightarrow 0$, for each sequence $(x_{n})_n\subseteq E$. For a net $(x_{\alpha})_{\alpha}\subseteq E$, if $x_{\alpha}\xrightarrow{un}0$ implies $Tx_{\alpha}\xrightarrow{un}0$, 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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Mina Matin, Kazem Haghnejad Azar, Razi Alavizadeh. 2019-08-08. Unbounded $\sigma$-order-to-norm continuous and $un$-continuous operators. https://arxiv.org/abs/1908.03192

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