Some relationship between G-frames and frames

Abstract

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.

Keywords

• Frame
• g-frame
• Hilbert C*-module
• g-frame operator
• Bounded operator