Duals and approximate duals of von Neumann–Schatten p-frames

Abstract

Abstract The purpose of this paper is to study duals and approximate duals of von Neumann–Schatten p-frames. We present a necessary and sufficient condition for the existence of a dual for a von Neumann–Schatten p-frame. Also, von Neumann–Schatten q-Riesz bases are characterized and it is shown that they share many useful properties with their corresponding notions in Hilbert spaces. Especially, it is focused on the uniqueness of their duals, and some equivalent conditions under which a von Neumann–Schatten p-frame admits a unique dual are derived. Moreover, approximate duality for von Neumann–Schatten p-Bessel sequences is introduced and some of the important properties of approximate duals are obtained, mainly their stability under different kinds of perturbations is considered.