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Hypocontinuity of multiplication on the Clifford algebra of an infinite-dimensional topological vector space

Author: Robert A. Haberstroh
Journal: Proc. Amer. Math. Soc. 50 (1975), 435-442
MSC: Primary 15A66; Secondary 46M99
MathSciNet review: 0379547
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Abstract: Given a quadratic form on an infinite-dimensional vector space $ E$, useful results have been obtained by imposing on $ E$ the linear topology $ t(V)$ described by Fischer and Gross [4], [5], [6], and investigated by Gross and Miller [9]. It has been shown that, in the induced topology, the Clifford algebra $ C(E)$ is a topological algebra, but that, for topologies strictly finer than $ t(V)$, multiplication need not be continuous. The main result of the present paper asserts that, even for topologies finer than $ t(V)$, desirable conclusions can be drawn if continuity is replaced by hypocontinuity (see [2] for definition).

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Keywords: Clifford algebra, linear topologies, hypocontinuity
Article copyright: © Copyright 1975 American Mathematical Society