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

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).