On $\mathfrak{I}$-reconstruction Property

Abstract

Reconstruction property in Banach spaces introduced and studied by Casazza and Christensen in [1]. In this paper we introduce reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property. A characterization of reconstruction property in Banach spaces which satisfy $\mathfrak{I}$-property in terms of frames in Banach spaces is obtained. Banach frames associated with reconstruction property are discussed.