VON NEUMANN–SCHATTEN p-FRAMES FOR OPERATORS

Abstract

We introduce von Neumann–Schatten $K$-$p$-frames and von Neumann–Schatten $K^{\ast }$-atomic systems, where $K$ is a bounded operator on a separable Banach space, and we collect some relationships between these two concepts. Also, we characterize von Neumann–Schatten $K$-$p$-frames in terms of a range inclusion property and show that they are stable under different kinds of perturbations and the action of some bounded operators. Moreover, we introduce and characterize the notions of $K$-duals and $K^{\ast }$-duals and obtain some of their properties.