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Structured triangular limit algebras

Published online by Cambridge University Press:  01 July 1997

DR Larson  and
B Solel
DR Larson
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA
B Solel
Affiliation:
Department of Mathematics, The Technion, Haifa 34000, Israel
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Abstract

We investigate a class of triangular UHF algebras which have the special property that there exists a sequence of unital multiplicative contractive finite-rank conditional expectations of the algebra into itself, which converges strongly to the identity, whose ranges form an increasing chain with dense union. A partial classification is given in terms of a local finiteness property, and a delimiting counterexample is obtained. Associated inverse limit algebras are considered, and a characterization of residually finite dimensional triangular AF algebras is obtained.

1991 Mathematics Subject Classification: 47D25, 46J35.

Keywords

limit algebrastriangularstructuredresidually finite dimensionalconditional expectation
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 75 , Issue 1 , July 1997 , pp. 177 - 193
Copyright
London Mathematical Society 1997

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