Woven fusion frames in Hilbert spaces

A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of introducing fusion frame or frame of subspace is to first construct local components and then build a global frame from these. This type of frame behaves as a generalization of frames. Motivating by the concepts of fusion and weaving frames, we investigate the notion woven-weaving fusion frames and present some of their features. Also, we study some effects of perturbations on woven frames and introduce Riesz decomposition of wovens and then we examine some of behaviors of this type of decomposition.