Some relationship between G-frames and frames

In this paper we proved that every g-Riesz basis for Hilbert space H with respect to K by adding a condition is a Riesz basis for Hilbert B(K)-module B(H,K). This is an extension of [A. Askarizadeh, M. A. Dehghan, {em G-frames as special frames}, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results for g-orthonormal and orthogonal bases. Some relationships between dual frame, dual g-frame and exact frame and exact g-frame are presented too.