On a Probabilistic Characterization of Hilbert Space

descriptionPublicationkeyboard_double_arrow_right Article 01 Mar 1977 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:Theory of Probability & Its Applications, volume 21, pages 410-412 (issn: 0040-585X, eissn: 1095-7219,

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Authors: Mushtari, D. Kh.;

doi: 10.1137/1121050

On a Probabilistic Characterization of Hilbert Space

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Abstract

Summary: 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 Freéchet spaces.

Keywords

Probability measures on topological spaces, Inner product spaces and their generalizations, Hilbert spaces, Generalized stochastic processes

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