Daws, M (2015) Non-commutative separate continuity and weakly almost periodicity for Hopf von Neumann algebras. Journal of Functional Analysis, 269 (3). pp. 683-704. ISSN 0022-1236
Abstract
For a compact Hausdorff space X, the space SC(X×X) of separately continuous complex valued functions on X can be viewed as a C*-subalgebra of C(X)**⊗-C(X)**, namely those elements which slice into C(X). The analogous definition for a non-commutative C*-algebra does not necessarily give an algebra, but we show that there is always a greatest C*-subalgebra. This thus gives a non-commutative notion of separate continuity. The tools involved are multiplier algebras and row/column spaces, familiar from the theory of Operator Spaces. We make some study of morphisms and inclusions. There is a tight connection between separate continuity and the theory of weakly almost periodic functions on (semi)groups. We use our non-commutative tools to show that the collection of weakly almost periodic elements of a Hopf von Neumann algebra, while itself perhaps not a C*-algebra, does always contain a greatest C*-subalgebra. This allows us to give a notion of non-commutative, or quantum, semitopological semigroup, and to briefly develop a compactification theory in this context.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015. Elsevier. Uploaded in accordance with the publisher's self-archiving policy. NOTICE: this is the author’s version of a work that was accepted for publication in 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, (2015) DOI:10.1016/j.jfa.2014.12.014 |
Keywords: | C*-bialgebra; Hopf von Neumann algebra; Separate continuity; Weakly almost periodic function |
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: | 13 Mar 2015 13:08 |
Last Modified: | 08 Mar 2016 21:57 |
Published Version: | http://dx.doi.org/10.1016/j.jfa.2014.12.014 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jfa.2014.12.014 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:83377 |