Compact-Like Operators in Lattice-Normed Spaces

Abstract

A linear operator $T$ between two lattice-normed spaces is said to be $p$-compact if, for any $p$-bounded net $x_{\alpha }$, the net $T{x}_{\alpha }$ has a $p$-convergent subnet. $p$-Compact operators generalize several known classes of operators such as compact, weakly compact, order weakly compact, $AM$-compact operators, etc. Similar to $M$-weakly and $L$-weakly compact operators, we define $p$-$M$-weakly and $p$-$L$-weakly compact operators and study some of their properties. We also study $up$-continuous and $up$-compact operators between lattice-normed vector lattices.

Cited by in corpus (1)

• $um$-Topology in multi-normed vector lattices