Hostname: page-component-84b7d79bbc-g5fl4 Total loading time: 0 Render date: 2024-07-28T20:28:54.070Z Has data issue: false hasContentIssue false

Kasparov's technical lemma for b*-algebras

Published online by Cambridge University Press:  04 October 2011

M. A. Hennings
Affiliation:
Sidney Sussex College, Cambridge CB2 3HU

Abstract

It is found that Kasparov's technical lemma may be proved for b*-algebras by a generalization of the techniques used in recent proofs for the C*-algebra case. An application of this result enables us to prove a standard lifting problem for b*-algebras.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1989

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Arveson, W.. Notes on extensions of C*-algebras. Duke Math. J. 44 (1977), 329355.CrossRefGoogle Scholar
[2] Arveson, W.. The harmonic analysis of automorphism groups. Proc. Sympos. Pure Math. 38 (1982), 199269.CrossRefGoogle Scholar
[3] Busby, R. C.. Double centralizers and extensions of C*-algebras. Trans. Amer. Math. Soc. 132 (1968), 7999.Google Scholar
[4] Hennings, M. A.. Double centralizers and the Tietze extension theorem for LMC*-algebras. (Preprint, 1987.)Google Scholar
[5] Higson, N.. On a technical theorem of Kasparov. J. Funct. Anal. 73 (1987), 107112.CrossRefGoogle Scholar
[6] Johnson, B. E.. An introduction to the theory of centralizers. Proc. London Math. Soc. (3) 14 (1964), 299320.CrossRefGoogle Scholar
[7] Olsen, C. L. and Pedersen, G. K.. A lifting problem for C*-algebras. (Presented to London Math. Soc. Symposium on Operator Algebras, Durham, 1987.)Google Scholar
[8] Pedersen, G. K.. C*-algebras and their Automorphism Groups. London Math. Soc. Monographs no. 14 (Academic Press, 1979).Google Scholar
[9] Phillips, N. C.. Inverse limits of C*-algebras. (Preprint, 1987.)Google Scholar
[10] Phillips, N. C.. Inverse limits of C*-algebras and applications. (Preprint, 1987.)Google Scholar
[11] Schmudgen, K.. Über LMC*-Algebren. Math. Nachr. 68 (1975), 167182.CrossRefGoogle Scholar
[12] Voiculescu, D.. Dual algebraic structures on operator algebras related to free products. J. Operator Theory 17 (1987), 8598.Google Scholar