1. Expansion of Bessel and g-Bessel sequences to dual frames and dual g-frames

M. S. Asgari; G. Kavian

Volume 02, Issue 01 , Winter 2013, , Pages 51-57

Abstract
  In this paper we study the duality of Bessel and g-Bessel sequences in Hilbert spaces. We show that a Bessel sequence is an inner summand of a frame and the sum of any Bessel sequence with Bessel bound less than one with a Parseval frame is a frame. Next we develop this results to the ...  Read More

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

S. S. Karimizad

Volume 02, Issue 01 , Winter 2013, , Pages 25-33

Abstract
  G-Frames in Hilbert spaces are a redundant set of operators which yield a representation 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 operators is a g-Bessel sequences if and only ...  Read More