This article is cited in 3 papers

Short Communications

On a probabilistic characterization of the Hilbert space

D. H. Muštari

Kazan

Abstract: Let, in a separable Banach space $E$, a countably-Hilbert topology can be introduced so that any continuous, with respect to this topology, generalized process, is extendable to a measure in $E'$. Then it is shown that the topology in $E$ is equivalent to a pre-Hilbert one.
This result is also generalized to Fréchet spaces.

Received: 28.10.1974

 English version: Theory of Probability and its Applications, 1977, 21:2, 410–412

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