Dilation of dual g-frames to dual g-Riesz bases

Abstract

In this paper, we study disjoint, strongly disjoint and weakly disjoint $g$-frames in Hilbert spaces and we provide necessary and sufficient conditions for disjointness, strongly disjointness and weakly disjointness of $g$-frames. Also, by using the orthogonal projections in Hilbert spaces, we prove that dual $g$-frames for a Hilbert space can be dilated to a $g$-Riesz basis for some larger Hilbert space and its dual $g$-Riesz basis.