Multipliers for von Neumann–Schatten Bessel sequences in separable Banach spaces

Abstract

In this paper we introduce the concept of von Neumann–Schatten Bessel multipliers in separable Banach spaces and obtain some of their properties. We study their behavior when the symbol belongs to ℓp. Also, we investigate the continuous dependency of Hilbert–Schmidt Bessel multipliers on their parameters. Special attention is devoted to the study of invertible Hilbert–Schmidt frame multipliers which is an extensive class of ordinary frame multipliers and includes g-frame multipliers and fusion frame multipliers as elementary examples. Among other things, the invertibility of Hilbert–Schmidt Riesz multipliers is completely characterized. In particular, we show that all the existing frames in Hilbert spaces is uniquely determined by the set of its dual frames.