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SIMULTANEOUS LIFTING FROM IRREDUCIBLE REPRESENTATIONS OF $C^*$-ALGEBRAS

Published online by Cambridge University Press:  31 January 2005

ROBERT ARCHBOLD  and
ALDO LAZAR
ROBERT ARCHBOLD
Affiliation:
Department of Mathematical Sciences, University of Aberdeen, King's College, Aberdeen AB24 3UE e-mail: [email protected]
ALDO LAZAR
Affiliation:
Department of Pure Mathematics, School of Mathematical Sciences, Tel Aviv University, Ramat Aviv, Israel 69978 e-mail: [email protected]
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Abstract

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Given a sequence $(\pi_n)$ of irreducible representations of a liminal $C^*$-algebra $A$, and a sequence $(b_n)$ of trace class operators with $b_n\in \pi_n(A)$, we investigate necessary conditions and sufficient conditions for the existence of a simultaneous lifting $a\in A$ such that, for each $n$, the trace of $\sigma(a)$ is bounded for irreducible representations $\sigma$ in a neighbourhood of $\pi_n$.

Keywords

46L0546L30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 195 - 204
Copyright
2005 Glasgow Mathematical Journal Trust