Isometric Reflection Vectors and Characterizations of Hilbert Spaces

Donghai Ji, Senlin Wu
2014 Journal of Function Spaces  
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.
doi:10.1155/2014/634082 fatcat:kbmx4vjp5jfppotbttqn6xunyu