DILATION AND DECOMPOSITION OF BESSEL SEQUENCES

There are several methods to show that every Bessel sequence or more specially every frame is the sum of several orthonormal basis. In this paper, every K-frame for H can be decomposed as an orthogonal sum of a tight frame sequence for H and a K-frame sequence for H. Also, we dilate every Bessel sequence for H to an orthonormal basis on a Hilbert space contains H.