Frame-related operators for woven frames

Abstract

A new notion in frame theory has been introduced recently under the name woven-weaving frames by Bemrose et al. In the study of frames, some operators like analysis, synthesis, Gram and frame operators play the central role. In this paper, for the first time, we introduce and define these operators for woven-weaving frames and review some of their properties. In continuation, we investigate the effect of different types of operators on the woven frames and their bounds. Also, we provide some conditions that shows sum of woven frames are also woven frames. Finally, we apply these properties with an example.