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

Subject Areas : History and biography

S. S. Karimizad ¹ (Department of Mathematics, Faculty of Science, Islamic Azad University, Central Tehran Branch, Tehran, Iran)

Received: 2013-01-01 Accepted : 2013-01-01 Published : 2013-03-01

Keywords: G-frames, G-Bessel sequences, G-orthonormal bases,

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 betweeng-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a boundedoperator.

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