SOME RELATIONSHIPS 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, G-frames as special frames, Turk. J. Math., 35, (2011) 1-11]. Also, we derived similar results forg-orthonormal and orthogonal bases. Some relationships between dual frame, dual g-frame and exact frame and exact g-frame arepresented too.