The reconstruction property in Banach spaces generated by matrices (Q2877572)

The reconstruction property for Banach spaces was introduced by \textit{P. G. Casazza} and \textit{O. Christensen} [Can. Math. Bull. 51, No. 3, 348--358 (2008; Zbl 1268.42053)]. In the paper under review, the authors introduce and study the Toeplitz reconstruction property in Banach spaces. They find a necessary condition for the existence of the Toeplitz reconstruction property and prove that the standard reconstruction property in a Banach space can generate the Toeplitz reconstruction property from a given Toeplitz matrix but not conversely. A Paley-Wiener type perturbation theorem for the Toeplitz reconstruction property is given. Sufficient conditions on infinite matrices to have the reconstruction property for a discrete signal space are obtained.