Operators Related to the Reconstruction Property in Banach Spaces

Abstract

Casazza and Christensen introduced the notion of the reconstruction property in separable Banach spaces, which is related to some deep concepts in Banach space theory. We discuss some types of operators associated with the reconstruction property and its related Banach frames in Banach spaces. It is shown that if a separable Banach space $$\mathcal {X}$$ admits the reconstruction property, then there exists an injective operator from an operator space into a sequence space related with the reconstruction property for $$\mathcal {X}$$ . Compact linear operators associated with the reconstruction property are discussed. Finally, we give two different sufficient conditions for Banach frames associated with the reconstruction property in terms of operators.