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The class of $p$-demicompact operators on lattice normed spaces

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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.

Abstract

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.

참고문헌 (28)

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