论文标题
向量空间上的半顺序连续运算符
Semi-order continuous operators on vector spaces
论文作者
论文摘要
在此手稿中，我们将研究$ \ tilde {o} $ - 在（部分）订购的向量空间中的收敛和矢量空间$ v $中的一种融合。矢量空间$ v $称为半顺序向量空间（在短半顺序中），如果存在有序的矢量空间$ w $，而从$ v $到$ w $的运算符$ t $。这样，我们说$ v $相对于$ \ {w，t \} $是半顺序的。 net $ \ {x_α\} \ subseteq v $被称为$ {\ {w，w，t \}} $ - 订购订单接收到v $中的向量$ x \（简而满足$y_β\ downarrow 0 $ in $ w $，对于每个$β$，都存在$α_0$，因此每当$ \ pm（tx_α-tx）\ leqy_β$时，只要$ a \ geqy_β$。在本手稿中，我们研究和研究$ \ {W，t \} $ - 收敛网的某些属性及其与其他顺序收敛的关系部分有序的向量空间。假设相对于$ \ {{w_1}，t_1 \} $和$ \ {w_2，t_2 \} $，$ v_1 $和$ v_2 $是半排序空格。从$ v_1 $到$ v_2 $的运算符$ s $称为半顺序连续，如果$x_α\ xrightArrow {\ {\ {{w_1}，t_1 \}} x $ ins $sx_α\sx_α\ xrightArrow { V_1 $。我们研究了这种新运营商的一些特性。
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.
