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On the commutant of...
On the commutant of C(X) in C*-crossed products by Z and their representations
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- Svensson, Christian (författare)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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Tomiyama, Jun (författare)
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(creator_code:org_t)
- Elsevier BV, 2009
- 2009
- Engelska.
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236. ; 256:7, s. 2367-2386
- Relaterad länk:
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http://dx.doi.org/10...
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Abstract
Ämnesord
Stäng
- 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 non-zero intersection with every non-zero, not necessarily closed or self-adjoint, 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.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Commutant
- Ideals
- Crossed product
- Dynamical system
- subalgebra
- Maximal abelian
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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