Affiliation:
1. Department of Applied Mathematics, Harbin University of Science and Technology, Harbin 150080, China
Abstract
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 sphereSXof a Banach spaceXhas nonempty interior inSX, thenXis 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.
Funder
National Natural Science Foundation of China