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COMPACT ELEMENTS AND OPERATORS OF QUANTUM GROUPS

Part of: Locally compact groups and their algebras Selfadjoint operator algebras Linear spaces and algebras of operators Abstract harmonic analysis

Published online by Cambridge University Press:  10 June 2016

MASSOUD AMINI ,
MEHRDAD KALANTAR ,
ALIREZA MEDGHALCHI ,
AHMAD MOLLAKHALILI  and
MATTHIAS NEUFANG
MASSOUD AMINI
Affiliation:
Department of Mathematics, Tarbiat Modares University, P.O.Box 14115-134, Tehran, Iran e-mail: mamini@modares.ac.ir
MEHRDAD KALANTAR
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences, ul. Sniadeckich 8, 00–956 Warszawa, Poland
ALIREZA MEDGHALCHI
Affiliation:
Department of Mathematics, Kharazmi University (Tarbiat Moallem University), 50, Taleghani Ave., 15618, Tehran, Iran e-mail: medghal2000@yahoo.com, ahmad.khalili1@gmail.com
AHMAD MOLLAKHALILI
Affiliation:
Department of Mathematics, Kharazmi University (Tarbiat Moallem University), 50, Taleghani Ave., 15618, Tehran, Iran e-mail: medghal2000@yahoo.com, ahmad.khalili1@gmail.com
MATTHIAS NEUFANG
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, CanadaK1S 5B6, and Université Lille 1 - Sciences et Technologies, U.F.R. de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d'Ascq Cédex, France e-mail: matthias.neufang@math.univ-lille1.fr
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Abstract

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A locally compact group G is compact if and only if its convolution algebras contain non-zero (weakly) completely continuous elements. Dually, G is discrete if its function algebras contain non-zero completely continuous elements. We prove non-commutative versions of these results in the case of locally compact quantum groups.

MSC classification

Primary: 46L89: Other “noncommutative” mathematics based on $C^*$-algebra theory 47L10: Algebras of operators on Banach spaces and other topological linear spaces 43A60: Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations 46L51: Noncommutative measure and integration 43A22: Homomorphisms and multipliers of function spaces on groups, semigroups, etc. 43A20: $L^1$-algebras on groups, semigroups, etc.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 445 - 462
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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