Daws, M and Salmi, P (2013) Completely positive definite functions and Bochner's theorem for locally compact quantum groups. Journal of Functional Analysis, 264 (7). 1525 - 1546 (22). ISSN 0022-1236
Abstract
We prove two versions of Bochner's theorem for locally compact quantum groups. First, every completely positive definite "function" on a locally compact quantum group $\G$ arises as a transform of a positive functional on the universal C*-algebra $C_0^u(\dual\G)$ of the dual quantum group. Second, when $\G$ is coamenable, complete positive definiteness may be replaced with the weaker notion of positive definiteness, which models the classical notion. A counterexample is given to show that the latter result is not true in general. To prove these results, we show two auxiliary results of independent interest: products are linearly dense in $\lone_\sharp(\G)$, and when $\G$ is coamenable, the Banach *-algebra $\lone_\sharp(\G)$ has a contractive bounded approximate identity.
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 Functional Analysis. 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 Journal of Functional Analysis, 264 (7). 1525 - 1546 (22) 2013 http://dx.doi.org/10.1016/j.jfa.2013.01.017 |
Keywords: | Bochner's theorem; Positive definite function; Quantum group |
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: | 16 Dec 2013 10:43 |
Last Modified: | 23 Jun 2023 21:36 |
Published Version: | http://dx.doi.org/10.1016/j.jfa.2013.01.017 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jfa.2013.01.017 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77162 |