Illinois Journal of Mathematics

On a quantum version of Ellis joint continuity theorem

Biswarup Das and Colin Mrozinski

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Abstract

We give a necessary and sufficient condition on a compact semitopological quantum semigroup which turns it into a compact quantum group. We give two applications of our results: a “noncommutative” version of Ellis joint continuity theorem for semitopological groups, a corollary to which is a new C∗-algebraic proof of the theorem for classical semitopological semigroup; we also investigate the question of the existence of the Haar state on a compact semitopological quantum semigroup and prove a “noncommutative” version of the converse Haar’s theorem.

Article information

Source
Illinois J. Math., Volume 59, Number 4 (2015), 839-858.

Dates
Received: 14 August 2015
Revised: 18 July 2016
First available in Project Euclid: 27 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1488186012

Digital Object Identifier
doi:10.1215/ijm/1488186012

Mathematical Reviews number (MathSciNet)
MR3628292

Zentralblatt MATH identifier
1358.81126

Subjects
Primary: 81R15: Operator algebra methods [See also 46Lxx, 81T05] 22A15: Structure of topological semigroups 22A20: Analysis on topological semigroups 42B35: Function spaces arising in harmonic analysis 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

Citation

Das, Biswarup; Mrozinski, Colin. On a quantum version of Ellis joint continuity theorem. Illinois J. Math. 59 (2015), no. 4, 839--858. doi:10.1215/ijm/1488186012. https://projecteuclid.org/euclid.ijm/1488186012


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