G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a repre- sentation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded opera- tors is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.