in this paper, we establish some new results in ultra bessel sequences and ultra bessel sequences of subspaces. also, we investigate ultra bessel sequences in direct sums of hilbert spaces.specially, we show that {( fi, gi)}∞ i=1 is a an ultra bessel sequencefor hilbert space h ⊕ k if and only if { fi}∞ i=1 and {gi}∞ i=1 are ultrabessel sequences for hilbert spaces h and k, respectively.

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization...

G-frames are natural generalizations of frames which cover many other recent generalizations of frames, e.g., bounded quasi-projectors, frames of subspaces, outer frames, oblique frames, pseudo-frames and a class of timefrequency localization operators. Moreover, it was shown that g-frames are equivalent to stable space splittings. In this paper, we study the stability of g-frames. We first pre...

Abstract G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that...

In representations using frames, oblique duality appears in situations where the analysis and synthesis has to be done different subspaces. some cases, we cannot obtain an explicit expression for duals others there exists only one dual frame which not properties need. Also, practice computations are exact. To give a solution these problems, this work introduce investigate notion of approximate ...