Daws, M and Runde, V (2010) Reiter's properties (P) and (P) for locally compact quantum groups. Journal of Mathematical Analysis and Applications, 364 (2). 352 - 365. ISSN 0022-247X
Abstract
A locally compact group G is amenable if and only if it has Reiter's property (P) for p = 1 or, equivalently, all p ∈ [1, ∞), i.e., there is a net (m) of non-negative norm one functions in L (G) such that lim sup {norm of matrix} L m - m {norm of matrix} = 0 for each compact subset K ⊂ G (L m stands for the left translate of m by x). We extend the definitions of properties (P) and (P) from locally compact groups to locally compact quantum groups in the sense of J. Kustermans and S. Vaes. We show that a locally compact quantum group has (P) if and only if it is amenable and that it has (P) if and only if its dual quantum group is co-amenable. As a consequence, (P) implies (P).
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | NOTICE: this is the author’s version of a work that was accepted for publication in the Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in the Journal of Mathematical Analysis and Applications, 364 (2) 2010 http://dx.doi.org/10.1016/j.jmaa.2009.11.036 |
Keywords: | Amenability; Co-amenability; Leptin's theorem; Locally compact quantum groups; Operator spaces; Reiter's property (P1); Reiter's property (P2) |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 20 Dec 2013 11:06 |
Last Modified: | 15 Sep 2014 02:35 |
Published Version: | http://dx.doi.org/10.1016/j.jmaa.2009.11.036 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jmaa.2009.11.036 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77178 |