اصغر رحیمی

The Gram matrix is defined for Bessel sequences by combining synthesis with subsequent analysis operators. If different sequences are used and an operator Uis inserted we reach so called U-cross Gram matrices. This can be seen as reinterpretation of the matrix representation of operators using frames. In this paper we investigate some necessary or sufficient conditions for Schatten p-class properties and the invertibility of U-cross Gram matrices. In particular, we show that under mild conditions the pseudo-inverse of a U-cross Gram matrix can always be represented as a U-cross Gram matrix with dual frames of the given ones. We link some properties of U-cross Gram matrices to approximate duals. Finally, we state several stability results. More precisely, it is shown that the invertibility of U-cross Gram matrices is preserved under small perturbations.