Portraits and perturbations of Hilbert-Schmidt frame sequences
The authors study perturbations in Hilbert-Schmidt frames (HS-frame). They prove that an arbitrary bounded invertible operator on \(l^2(J)\) transforms a HS-frame into another HS-frame and also present a sufficient condition on bounded operators on \(l^2(J)\) which transform an \(l^2(J)\)-decomposable HS-frame into another HS-frame (HS-Riesz basis, HS-frame sequence and HS-Riesz sequence). They further prove that suitably perturbing a HS-frame sequence (HS-Riesz sequence) leaves a HS-frame sequence (HS-Riesz sequence).
scientific article; zbMATH DE number 7610167
scientific article