@article { author = {Rashidi-Kouchi, Mehdi and Nazari, Akbar}, title = {Some relationship between G-frames and frames}, journal = {Sahand Communications in Mathematical Analysis}, volume = {02}, number = {1}, pages = {1-7}, year = {2015}, publisher = {University of Maragheh}, issn = {2322-5807}, eissn = {2423-3900}, doi = {}, 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}, url = {https://scma.maragheh.ac.ir/article_11699.html}, eprint = {https://scma.maragheh.ac.ir/article_11699_ca0b66c4ecad6b41c794d5d431bf3ae4.pdf} }