  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.
