IJPAM: Volume 37, No. 1 (2007)


S.K. Kaushik$^1$, Ghanshyam Singh$^2$, Virender$^3$
$^1$Department of Mathematics
Kirori Mal College
University of Delhi
Delhi, 110 007, INDIA
e-mail: shikk2003@yahoo.co.in
$^{2,3}$Department of Mathematics and Statistics
College of Science
M.L.S. University
Udaipur (Rajasthan), INDIA
$^2$e-mail: Ghanshyamsrathore@yahoo.co.in
$^3$e-mail: virender57@yahoo.com

Abstract.Perturbation of frames in Hilbert spaces by a non-zero element has been considered. Examples has been given to establish that such a perturbation need not be a frame. It has been proved that the perturbation of a near exact frame by a non-zero element is not a frame. Also perturbation of a frame $\{x_n\}$ of the type $\{x_n + c_n x_0\}$, where $x_0$ is a non-zero element and $\{c_n\}$ is any sequence of scalars has been considered and a sufficient condition for this type of perturbation to be a frame has been given. Finally, perturbation of a frame by a finite set of linearly independent elements has been considered and a sufficient condition for the same has been given.

Received: March 1, 2007

AMS Subject Classification: 42C15

Key Words and Phrases: frames, near exact frames, Bessel sequences, perturbation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 37
Issue: 1