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Representations of involutive semigroups

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Abstract

Involutive [topological] semigroups are semigroups endowed with an involutive antiautomorphism. A representation of such a semigroup means an involution preserving [weakly continuous] morphism into the algebra of bounded operators on a Hilbert space. We develop a representation theory of involutive [topological] semigroups based on positive definite functions on them. We do not generally assume the existence of an identity element. This makes the proofs of some results harder, but most results hold in this general setting.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Karl-Hermann Neeb

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  1. Karl-Hermann Neeb
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Communicated by Karl H. Hofmann

The author thanks the referee for many constructive suggestions to improve the exposition of the paper.

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Neeb, KH. Representations of involutive semigroups. Semigroup Forum 48, 197–218 (1994). https://doi.org/10.1007/BF02573670

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  • DOI: https://doi.org/10.1007/BF02573670

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