Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T13:31:58.326Z Has data issue: false hasContentIssue false
  • English
  • Français

Hilbert C*-modules and conditional expectations on crossed products

Part of: Selfadjoint operator algebras Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Mahmood Khoshkam
Mahmood Khoshkam
Affiliation:
Department of Mathematics and Statistics University of Saskatchewan106 Wiggins Road Saskatoon, SK S7N 5E6Canada e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we study the structure of certain conditional expectation on crossed product C*-algebra. In particular, we prove that the index of a conditional expectation E: B → A is finite if and only if the index of the induced expectation from B ⋊ G onto A ⋊ G is finite where G is a discrete group acting on B.

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46H25: Normed modules and Banach modules, topological modules (if not placed in or )
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 1 , August 1996 , pp. 106 - 118
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Blackadar, B., ‘Subalgebras of C*-algebras’, J. Operator Theory 14 (1985), 374–350.Google Scholar
[2]Choda, H., ‘A correspondence between subgroups and subalgebras in a C*-crossed product’, Proc. Sympos. Pure Math. 38 Part I (Amer. Math. Soc., Providence, 1982), 375–377.CrossRefGoogle Scholar
[3]Choi, M. D., ‘A simple C*-algebra generated by two finite order unitaries’, Canad. J. Math. 31 (1979), 867–880.Google Scholar
[4]Connes, A., ‘An analogue of the Thom isomorphism for crossed products of a C*-algebra by an action of R’, Adv. Math. 39 (1981), 31–55.Google Scholar
[5]Green, P., ‘The local structure of twisted covariance algebras’, Acta Math. 140 (1978), 191–250.Google Scholar
[6]Green, P., ‘The structure of imprimitivity algebras’, J. Funct. Anal. 36 (1980), 88–104.Google Scholar
[7]Jones, V., ‘Index for subfactors’, Invent. Math. 72 (1983), 1–25.CrossRefGoogle Scholar
[8]Kasparov, G. G., ‘Hilbert C*-modules: theorems of Stinespring and Voiculescu’, J. Operator Theory 4 (1980), 133–150.Google Scholar
[9]Kasparov, G. G., ‘Equivariant KK-theory and the Novikov Conjecture’, Invent. Math. 41 (1988), 141–201.Google Scholar
[10]Pedersen, G., C*-algebras and their automorphism groups (Academic Press, London, 1979).Google Scholar
[11]Pimsner, M. and Popa, S., ‘Entropy and index for subfactors’, Ann. Sci. Écol. Norm. Sup. 19 (1986), 57–106.Google Scholar
[12]Rieffel, M., ‘Induced representations of C*-algebras’, Adv. Math. 13 (1974), 176–257.Google Scholar
[13]Tomiyama, J., Invitation to C*-algebras and topological dynamics (World Scientific, Singapore, 1987).CrossRefGoogle Scholar
[14]Umegaki, H., ‘Conditional expectation on operator algebras’, Tôhoku Math. J. 6 (1954), 358–362.Google Scholar
[15]Watatani, Y., Index for C*-subalgebras, Mem. Amer. Math. Soc. 424 (Amer. Math. Soc., Providence, 1990).Google Scholar