%0 Journal Article
%T Besselian $G$-frames and Near $G$-Riesz bases
%A M. R. Abdollahpour
%A A. Najati
%J Applicable Analysis and Discrete Mathematics
%D 2011
%I University of Belgrade and Academic Mind
%R 10.2298/aadm110510013a
%X In this paper we introduce and study near g-Riesz basis, Besselian g-frames and unconditional g-frames. We show that a near g-Riesz basis is a Besselian g-frame and we conclude that under some conditions the kernel of associated synthesis operator for a near g-Riesz basis is finite dimensional. Finally, we show that a g-frame is a g-Riesz basis for a Hilbert space H if and only if there is an equivalent inner product on H, with respect to which it becomes an g-orthonormal basis for H.
%K g-Bessel sequence
%K g-frame
%K Besselian g-frame
%K near g-Riesz basis
%U http://pefmath.etf.rs/vol5num2/AADM-Vol5-No2-259-270.pdf