A measure-theoretic characterization of inner product spaces

Rok, strany: 1997, 273 - 280

We show that if $E$ is an infinite-dimensional generalized inner product space over a division ring $K$ with a Hermitian form on $E$ such that in any direction there is a unit vector, then the existence of at least one finitely additive measure (= state) on the set of all orthogonally closed subspaces which is concentrated on some one-dimensional subspace entails that the division ring is either the ring of all real, complex or quaternionic numbers, and $E$ is a Hilbert space over $K$.

ISO 690:

Dvurečenskij, A. 1997. A measure-theoretic characterization of inner product spaces. In Tatra Mountains Mathematical Publications, vol. 10, no.1, pp. 273-280. 1210-3195.

APA:

Dvurečenskij, A. (1997). A measure-theoretic characterization of inner product spaces. Tatra Mountains Mathematical Publications, 10(1), 273-280. 1210-3195.