g-(M,µ)-Frames in Hilbert Spaces1

Let (M,µ) be a measure space, U and V be two Hilbert Spaces. In this paper, we introduce and discuss g-(M,µ)-frames {Λm}m∈M for a Hilbert Space U with respect to a family of subspaces {Vm}m∈M of V and then we characterize the properties of g-(M,µ)-frames and dual of g-(M,µ)-frames. Finally, we generalize the perturbations of (M,µ)-frames and g-frames to g-(M,µ)-frames and derive some meaningful results