On abstract results of operator representation of frames in Hilbert spaces

In this paper, we give a multiplication operator representation of bounded self-adjoint operators T on a Hilbert space H such that – is a frame for H, for some – . We state a necessary condition in order for a frame – to have a representation of the form – . Frame sequence – with the synthesis operator U, have also been characterized in terms of the behavior spectrum of – . Next, using the operator response of an element with respect to a unit vector in H, frames – of the form – are characterized. We also consider stability frames as – . Finally, we conclude this note by raising a conjecture connecting frame theory and operator theory