We show that reﬂexivity of a Banach space can be characterized by a simple property formulated in terms of the distance to the intersection of a decreasing countable family of closed subspaces. We provide some explicit examples of the failure of the property in the non-reﬂexive case.
Cite this article
Gerardo Chacón, Vicente Montesinos, Alfredo Octavio, A Note on the Intersection of Banach Subspaces. Publ. Res. Inst. Math. Sci. 40 (2004), no. 1, pp. 1–6DOI 10.2977/PRIMS/1145475964