Banach frames and atomic decompositions in the space of bounded operators on Hilbert spaces

The concept of frames is used extensively for the representation of signal or functions. Recently, this concept is applied more and more for the representation of operators, both in theory as well as in the application for the numerical solutions of operator equations. In this paper we first give a survey about the matrix representation of operators using frames. Then we prove that the tensor product of frames forms a Banach frame and an atomic decomposition for the space of bounded operators of Hilbert spaces.