Toeplitz $O$-Frames for Operators in Banach Spaces (Analysis in Theory and Applications, 2025)
We define Toeplitz $O$-frame for operators as a generalization of the notionof $O$-frame introduced by Reinov [11]. A necessary condition for the existence ofa Toeplitz $O$-frame is given. It has been proved that an $O$-frame for operators cangenerate a Toeplitz $O$-frame from a given Toeplitz matrix but the converse need not betrue. Also, a sufficient condition on infinite matrices for the existence of an $O$-frame isgiven. Finally, the notion of a strong $O$-frame is defined and a necessary and sufficientcondition for its existence has been obtained.
Keywords: Frames; operators; $O$-frames.