Kyoto Journal of Mathematics

Duality theorem for topological semigroups

Nobuhiko Tatsuuma

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

duality theory Tannaka-type duality theory topological semigroups


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

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  • [1] N. Bourbaki, Topologie générale, chapitre 2, Hermann, Paris, 1951.
  • [2] N. Tatsuuma, A duality theorem for locally compact groups, J. Math. Kyoto Univ. 6 (1967), 187–293.
  • [3] N. Tatsuuma, “Duality theorem for inductive limit group of direct product type” in Representation Theory and Analysis on Homogeneous Spaces, RIMS Kôkyûroku Bessatsu B7, Res. Inst. Math. Sci. (RIMS), Kyoto, 2008, 13–23.
  • [4] N. Tatsuuma, Duality theorem for inductive limit groups, Kyoto J. Math. 54 (2014), 51–73.
  • [5] N. Tatsuuma, Duality theorems and topological structure of groups, Kyoto J. Math. 54 (2014), 75–101.
  • [6] K. Yosida, Functional Analysis, Springer, Berlin, 1971.