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Recently, a new application of frame theory in Hilbert spaces has been emerged related to distributed signal processing. Bemrose et al. [4] have developed a theory of weaving frames to handle such types of problems. In this article, we introduce and study woven pg-frames for Banach spaces. It has been shown that a family of pg-Bessel sequences is always woven Bessel family. The image of woven pg-frame under a bounded invertible operator is a woven pg-frame has been proved. Also, a necessary and sufficient condition for the image of woven pg-frame under a bounded operator to be a woven pg-frame has been given. Further, some characterizations of woven pg-frames and characterization of woven pg-Bessel sequences are given. Furthermore, woven qg-Riesz bases are defined and prove that these are particular cases of woven pg-frames. Finally, some equivalent conditions for woven qg-Riesz basis are given. [ABSTRACT FROM AUTHOR]

In this paper, we give characterizations of retro Banach frames in Banach spaces. The notion of almost exact retro Banach frame is defined and a characterization of retro Banach frame has been given. Also results exhibiting relationship between frames, almost exact retro Banach frames and Riesz bases has been proved. Finally, we give some perturbation results of retro Banach frames and an almost exact retro Banach frames for Banach spaces. [ABSTRACT FROM AUTHOR]

Casazza and Christensen in [5], introduced and studied the reconstruction property in Banach spaces. In this paper sufficient conditions for the existence of the reconstruction property in Banach spaces are obtained. Casazza and Christensen gave Paley-Wiener type perturbation of the reconstruction property which does not force equivalence of the sequences. Some Paley-Wiener type perturbations concerning the reconstruction property are discussed. Motivated by a paper by Holub [18], the notion of Besselian type reconstruction property in Banach spaces is introduced and its application to Banach frames is obtained. [ABSTRACT FROM AUTHOR]