New aspects of weaving K-frames: the excess and duality

Authors : Elahe Agheshteh Moghaddam, Ali Akbar Arefijamaal

Pages : 652-666

Doi:10.15672/hujms.1008448

View : 136 | Download : 203

Publication Date : 2024-06-27

Article Type : Research Paper

Abstract :Weaving frames in separable Hilbert spaces have been recently introduced by Bemrose et al. to deal with some problems in distributed signal processing and wireless sensor networks. Likewise weaving K -frames have been proved to be useful during signal reconstructions from the range of a bounded linear operator K. In this paper, we study the notion of weaving and its connection to the duality of K-frames and construct several pairs of woven K-frames. Also, we find a unique biorthogonal sequence for every K-Riesz basis and obtain a $K^*$-frame which is woven by its canonical dual. Moreover, we describe the excess for K-frames and prove that any two woven K-frames in a separable Hilbert space have the same excess. Finally, we introduce the necessary and sufficient condition under which a K-frame and its image under an invertible operator have the same excess.
Keywords : frames, dual frames, Riesz bases, woven frames, excess of frames, K frames