On the commutant of C(X) in C*crossed products by Z and their representations
(2009) In Journal of Functional Analysis 256(7). p.23672386 Abstract
 For the C*crossed product C*(Sigma) associated with an arbitrary topological dynamical system Sigma = (X, sigma), we provide a detailed analysis of the commutant, in C*(Sigma), of C(X) and the commutant of the image of C(X) under an arbitrary Hilbert space representation (pi) over tilde of C*(E), In particular, we give a concrete description of these commutants, and also determine their spectra. We show that, regardless of the system E, the commutant of C(X) has nonzero intersection with every nonzero, not necessarily closed or selfadjoint, ideal of C*(Z). We also show that the corresponding statement holds true for the commutant of (pi) over tilde (C(X)) tinder the assumption that a certain family of pure states of (pi) over tilde... (More)
 For the C*crossed product C*(Sigma) associated with an arbitrary topological dynamical system Sigma = (X, sigma), we provide a detailed analysis of the commutant, in C*(Sigma), of C(X) and the commutant of the image of C(X) under an arbitrary Hilbert space representation (pi) over tilde of C*(E), In particular, we give a concrete description of these commutants, and also determine their spectra. We show that, regardless of the system E, the commutant of C(X) has nonzero intersection with every nonzero, not necessarily closed or selfadjoint, ideal of C*(Z). We also show that the corresponding statement holds true for the commutant of (pi) over tilde (C(X)) tinder the assumption that a certain family of pure states of (pi) over tilde (C*(Z)) is total. Furthermore we establish that, if C(X) subset of C(X)', there exist both a C*Kibalgebra properly between C(X) and C(X)' which has the aforementioned intersection property, and such a C*subalgebra which does not have this properly. We also discuss existence of* a projection of norm one from C*(Sigma) onto the commutant of C(X). (c) 2009 Elsevier Inc. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1404780
 author
 Svensson, Christian ^{LU} and Tomiyama, Jun
 organization
 publishing date
 2009
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Commutant, Ideals, Crossed product, Dynamical system, subalgebra, Maximal abelian
 in
 Journal of Functional Analysis
 volume
 256
 issue
 7
 pages
 2367  2386
 publisher
 Elsevier
 external identifiers

 wos:000264078100012
 scopus:60649095407
 ISSN
 00221236
 DOI
 10.1016/j.jfa.2009.02.002
 language
 English
 LU publication?
 yes
 id
 8b345789a93044a6be0d946faf04e1a6 (old id 1404780)
 date added to LUP
 20160401 14:22:12
 date last changed
 20210303 05:09:27
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