Document Type : Research Paper


1 Department of Mathematics, Islamic Azad University, Kahnooj Branch, Kahnooj, Iran.

2 Department of Mathematics, Shahid Bahonar University, Kerman, Iran.


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.


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