## Kyoto Journal of Mathematics

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

### Duality theorem for topological semigroups

#### 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

**Subjects**

Primary: 22A25: Representations of general topological groups and semigroups 22D35: Duality theorems

**Keywords**

duality theory Tannaka-type duality theory topological semigroups

#### 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