Bessel sequence and finite normalized tight frames

In this article, we show that a finite dimensional Hilbert space can have an infinite Bessel sequence, but a normalized Bessel sequence in a finite dimensional Hilbert space must be of finite length. A relation between the dimension of a given finite dimensional Hilbert space and the bound of any finite normalized tight frame for the underlying space is obtained. Also some properties of the frame operator and the Bessel sequence are discussed for finite normalized tight frame with some examples.