g-ORTHONORMAL BASES, g-RIESZ BASES AND g-DUAL OF g-FRAMES

The duals of frames, duals of g-frames, and orthonormal bases are widely used in mathematics, physics, signal processing, and many other areas, in which elements need to be represented in terms of the frame, g-frame, and basis elements. In this paper, we give equivalent conditions for a g-orthonormal basis and characterize all g-Riesz bases for a separable Hilbert space J-C, starting with a given g-orthonormal basis. Also, we introduce the notion of generalized dual of a g-frame in a separable Hilbert space J-C and provide some characterizations of the generalized dual of g-frames. Our results generalize and improve the results obtained by Dehgan and Hasankhani Fard in [1].