On the Class of p-M-Weakly Demicompact Operators with Numerical Application

Abstract

In this paper, we introduce a new class of operators, called p-M-weakly demicompact operators (PMWD), within the framework of lattice-normed vector lattices. This new concept generalizes classical notions such as weak compactnessand demicompactness by incorporating both the lattice structure and a vectorvalued lattice norm. We establish relationships with the classes of p-compact andp-M-weakly compact operators, as well as their stability under perturbations. Weuse mixed-norm techniques to relate PMWD operators to M-weakly demicompactoperators in mixed-normed settings. We give a numerical application of the stabilityof hidden states in neural networks.