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Topological Partial *-Algebras: Basic Properties and Examples

Profile image of Jean-pierre AntoineJean-pierre Antoine

1999, Reviews in Mathematical Physics

https://doi.org/10.1142/S0129055X99000106
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40 pages

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Abstract

Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).

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Related topics

  • Function Space
  • inner product space

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