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Abstract. The reconstruction property for Banach spaces was introduced by Casazza and Christensen. In this paper we give a type of the reconstruction property in Banach spaces which is generated by the Toeplitz matrices and we call it the Toeplitz reconstruction property. It is proved that the standard reconstruction property in a Banach space can generate the Toeplitz reconstruction property from a given Toeplitz matrix but not conversely. Sufficient conditions on infinite matrices to have the reconstruction property for a discrete signal space are given.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Aug 1, 2014
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