Generalized fusion frame and some of their properties in tensor product Hilbert spaces are described. Also, the canonical dual g-fusion is considered. Finally, operator for a pair Bessel sequences presented.

In this paper, we study approximate duals of $g$-frames and fusion frames in Hilbert $C^ast-$modules. We get some relations between approximate duals of $g$-frames and biorthogonal Bessel sequences, and using these relations, some results for approximate duals of modular Riesz bases and fusion frames are obtained. Moreover, we generalize the concept of $Q-$approximate duality of $g$-frames and ...

We introduce the notion of a g-atomic subspace for bounded linear operator and construct several useful resolutions identity on Hilbert space using theory g-fusion frames. Also we shall describe concept frame pair Bessel sequences some their properties.

In this paper we consider perturbation of Xd-Bessel sequences, Xdframes, Banach frames, atomic decompositions and Xd-Riesz bases in separable Banach spaces. Equivalence between some perturbation conditions is investigated.

By considering a particular probabilistic scenario associated with coincidences, we are led to a family of functions akin to the modified Bessel function of the first kind. These are in turn solutions to a certain family of linear differential equations possessing structural similarities to the modified Bessel differential equation. The Stirling number triangle of the second kind arises quite n...