A. Khosravi

We use two appropriate bounded invertible operators to define a controlled fusion frame with optimal fusion frame bounds to improve the numerical efficiency of iterative algorithms for inverting the fusion frame operator. We show that controlled fusion frames as a generalization of fusion frames give a generalized way to obtain numerical advantage in the sense of preconditioning to check the fusion frame condition. Also, we consider locally controlled frames for each locally space to obtain new globally controlled frames for our Hilbert space. We develop some well known results in fusion frames to the controlled fusion frames case.

g-frames and fusion frames in Hilbert C*-modules have been defined by the second author and B.~Khosravi in [15] and operator-valued frames in Hilbert C*-modules have been defined by Kaftal et al in [11]. We show that every operator-valued frame is a g-frame, we also show that in Hilbert C*-modules tensor product of orthonormal basis is an orthonormal basis and tensor product of g-frames is a g-frame, we get some relations between their g-frame operators, and we study tensor product of operator-valued frames in Hilbert C*-modules.