Document Type : Research Paper
Authors
Department of Mathematics, University of Mohaghegh Ardabili, P.O.Box 179, Ardabil, Iran.
Abstract
In this paper, we show that in each finite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a finite dimensional Hilbert space has frameness bound.
Keywords
[1] M. R. Abdollahpour and A. Shekari, Ultra Bessel sequence of subspaces in Hilbert spaces, preprint.
[2] P. G. Casazza and G. Kutynoik, Frames of subspaces, Wavelets, Frames and Operator Theory (College Park, MD, 2003), 87-113, Contemp. Math. 345, Amer. Math. Soc., Providence, RI, 2004.
[3] O. Christencen, An introduction to frames and Riesz bases, Birkhauser, Boston, 2003.
[4] M. H. Faroughi and A. Najati, Ultra Bessel sequences in Hilbert Spaces, South-east Asian Bulletin of Mathematics, 32 (2008) 425-436.
[2] P. G. Casazza and G. Kutynoik, Frames of subspaces, Wavelets, Frames and Operator Theory (College Park, MD, 2003), 87-113, Contemp. Math. 345, Amer. Math. Soc., Providence, RI, 2004.
[3] O. Christencen, An introduction to frames and Riesz bases, Birkhauser, Boston, 2003.
[4] M. H. Faroughi and A. Najati, Ultra Bessel sequences in Hilbert Spaces, South-east Asian Bulletin of Mathematics, 32 (2008) 425-436.
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