Ultra Bessel Sequences in Hilbert Spaces.

In this paper, we shall introduce ultra Bessel sequences in separable Hilbert spaces (i.e., Bessel sequences with uniform convergence property) and we shall see that no frame in an infinite dimonsional Hilbert space can be an ultra Bessel sequence, but each frame in a finite dimension Hilbert space is an ultra Bessel sequence . We shall also show that for each frame in a finite dimensional Hilbert space there exists a bound of frameness. [ABSTRACT FROM AUTHOR]