## Kyoto Journal of Mathematics

### Duality theorem for topological semigroups

Nobuhiko Tatsuuma

#### Abstract

For topological semigroups $S$, we consider Tannaka-type duality theorems, which are extensions of the notion of weak Tannaka duality theorem for topological groups. In the case of topological semigroups, we must set as the dual object of $S$ all isometric representations of $S$ instead of all unitary representations. We define a property T-type for $S$. After arguments analogous to previous work from the author, we can prove that our Tannaka-type duality theorem is valid if and only if $S$ is a T-type semigroup.

#### Article information

Source
Kyoto J. Math., Volume 55, Number 3 (2015), 543-554.

Dates
Received: 18 September 2012
Revised: 21 January 2014
Accepted: 3 June 2014
First available in Project Euclid: 9 September 2015

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1441824034

Digital Object Identifier
doi:10.1215/21562261-3089046

Mathematical Reviews number (MathSciNet)
MR3395976

Zentralblatt MATH identifier
06489504

#### Citation

Tatsuuma, Nobuhiko. Duality theorem for topological semigroups. Kyoto J. Math. 55 (2015), no. 3, 543--554. doi:10.1215/21562261-3089046. https://projecteuclid.org/euclid.kjm/1441824034

#### References

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• [5] N. Tatsuuma, Duality theorems and topological structure of groups, Kyoto J. Math. 54 (2014), 75–101.
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