Isometric Reflection Vectors and Characterizations of Hilbert Spaces

Abstract EN

A known characterization of Hilbert spaces via isometric reflection vectors is based on the following implication: if the set of isometric reflection vectors in the unit sphere S X of a Banach space X has nonempty interior in S X , then X is a Hilbert space.

Applying a recent result based on well-known theorem of Kronecker from number theory, we improve this by substantial reduction of the set of isometric reflection vectors needed in the hypothesis.