The invertibility of \(U\)-fusion cross Gram matrices of operators (Q2006910)

In this paper, the authors consider U-fusion cross Gram matrices and investigate (pseudo-)invertibility of U-fusion Gram matrices of operators for a bounded operator U. They provide the necessary and sufficient conditions for the (pseudo-)invertibility of the U-cross Gram matrices. Also, they characterize fusion orthonormal bases and fusion Riesz bases by those properties and present explicit formulas for the (pseudo-)inverses. Finally, the authors investigate which perturbations of fusion Bessel sequences preserve the invertibility of the fusion Gram matrix of operators and discuss some stability results for U-cross Gram matrices of operators.