(untitled) (Analysis in Theory and Applications, 2025)
We define Toeplitz O-frame for operators as a generalization of the notion of O-frame introduced by Reinov [11]. A necessary condition for the existence of a Toeplitz O-frame is given. It has been proved that an O-frame for operators can generate a Toeplitz O-frame from a given Toeplitz matrix but the converse need not be true. Also, a sufficient condition on infinite matrices for the existence of an O-frame is given. Finally, the notion of a strong O-frame is defined and a necessary and sufficient condition for its existence has been obtained.