Title: 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 $Tx_\alpha$ 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.