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arXiv · 0904.0894

Topological partial *-algebras: Basic properties and examples

J. -P. Antoine·F. Bagarello·C. Trapani
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Abstract

Let $A$ be a partial *-algebra endowed with a topology $τ$ that makes it into a locally convex topological vector space $A[τ]$. Then $A$ 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 $A$ 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 $L^p$ spaces on $[0,1]$ or on $\mathbb R$, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).

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J. -P. Antoine, F. Bagarello, C. Trapani. 2009-04-06. Topological partial *-algebras: Basic properties and examples. https://arxiv.org/abs/0904.0894

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