The study on controlled g-frames and controlled fusion frames in Hilbert C*-modules

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*-algebra rather than in the field of complex numbers.In this paper, we define and characterize controlled g-frames and controlled fusion frames in Hilbert C*-modules. These are generalization of controlled frames in Hilbert C*-modules and also controlled g-frames and controlled fusion frames in Hilbert spaces. We show, similar in Hilbert space, every controlled g-frame in Hilbert C*-module is an usual g-frame. Also we study the relation between controlled fusion frames and fusion frames in Hilbert C*-modules. Finally we present a sufficient condition on a family of closed submodules to be a controlled fusion frame.