Communications of the
Korean Mathematical Society CKMS

In the present paper, we introduce a new class of operators called $p$-demicompact operators between two lattice normed spaces $X$ and $Y$. We study the basic properties of this class. Precisely, we give some conditions under which a $p$-bounded operator be $p$-demicompact. Also, a sufficient condition is given, under which each $p$-demicompact operator has a modulus which is $p$-demicompact. Further, we put in place some properties of this class of operators on lattice normed spaces.

Keywords: $p$-demicompact, demicompact operator, Banach lattice, vector lattice, lattice-normed space, $p$-convergence

MSC numbers: 46A40, 46B40, 46B42