arXiv 2006.040652020-06-07math.FA

向量空间上的半序连续算子

Semi-order continuous operators on vector spaces

Kazem Haghnejad Azar, Mina Matin, Razi Alavizadeh

摘要：

本文研究了（偏序）向量空间中的$\tilde{o}$ -收敛和向量空间$V$中的一类收敛。一个向量空间$V$称为半序向量空间（简称半序空间），如果存在一个序向量空间$W$和一个从$V$到$W$的算子$T$。这样，我们说$V$是关于$\{W, T\}$的半序空间。一个净$\{x_α\}\subseteq V$被称为${\{W,T\}}$阶收敛到一个向量$x\in V$（简而言之我们写$x_α\xrightarrow {\{W, T\}}x$），只要在$W$中存在一个净$\{y_β\}$满足$W$中的$y_β\downarrow 0$，并且对于每个$β$，存在$α_0$使得$\pm (Tx_α-Tx) \leq y_β$只要$α\geq α_0$ .本文研究了偏序向量空间中$\{W,T\}$ -收敛网的一些性质及其与其它序收敛的关系。假设$V_1$和$V_2$分别是关于$\{{W_1}, T_1\}$和$\{W_2, T_2\}$的半序空间。从$V_1$到$V_2$的算子$S$称为半序连续的，如果$x_α\xrightarrow {\{{W_1}, T_1\}}x$在任何时候都蕴涵$Sx_α\xrightarrow {\{W_2, T_2\}}Sx$，则$\{x_α\}\subseteq V_1$。我们研究了这种新的分类算子的一些性质。

英文摘要：

In this manuscript, we will study both $\tilde{o}$-convergence in (partially) ordered vector spaces and a kind of convergence in a vector space $V$. A vector space $V$ is called semi-order vector space (in short semi-order space), if there exist an ordered vector space $W$ and an operator $T$ from $V$ into $W$. In this way, we say that $V$ is semi-order space with respect to $\{W, T\}$. A net $\{x_α\}\subseteq V$ is said to be ${\{W,T\}}$-order convergent to a vector $x\in V$ (in short we write $x_α\xrightarrow {\{W, T\}}x$), whenever there exists a net $\{y_β\}$ in $W$ satisfying $y_β\downarrow 0$ in $W$ and for each $β$, there exists $α_0$ such that $\pm (Tx_α-Tx) \leq y_β$ whenever $α\geq α_0$. In this manuscript, we study and investigate some properties of $\{W,T\}$-convergent nets and its relationships with other order convergence in partially ordered vector spaces. Assume that $V_1$ and $V_2$ are semi-order spaces with respect to $\{{W_1}, T_1\}$ and $\{W_2, T_2\}$, respectively. An operator $S$ from $V_1$ into $V_2$ is called semi-order continuous, if $x_α\xrightarrow {\{{W_1}, T_1\}}x$ implies $Sx_α\xrightarrow {\{W_2, T_2\}}Sx$ whenever $\{x_α\}\subseteq V_1$. We study some properties of this new classification of operators.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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