LAUSR

For applications like the numerical solution of physical equations a discretization scheme for operators is necessary. Recently frames have been used for such an operator representation. In this paper, we interpret the operator representation using fusion frames as a generalization of fusion Gram matrices. We present the basic definition of U-fusion cross Gram matrices of operators for bounded operator U. We give sufficient conditions for their invertibility. In particular, we characterize fusion Riesz bases and fusion orthonormal bases by such matrices. Finally, we look at which perturbation of fusion Bessel sequences preserve the invertibility of the Gram fusion matrix of operators.