GENERALIZED FRAMES IN HILBERT SPACES

Here, we develop the generalized frame theory. We introduce two methods for generating g-frames of a Hilbert space H. The first method uses bounded linear operators between Hilbert spaces. The second method uses bounded linear operators on l(2) to generate g-frames of H. We characterize all the bounded linear mappings that transform g-frames into other g-frames. We also characterize similar and unitary equivalent g-frames in term of the range of their linear analysis operators. Finally, we generalize the fundamental frame identity to g-frames and derive some new results.