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Structured Triangular Limit Algebras
Author(s) -
Larson DR,
Solel B
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000312
Subject(s) - mathematics , multiplicative function , counterexample , limit (mathematics) , pure mathematics , class (philosophy) , identity (music) , triangular matrix , rank (graph theory) , property (philosophy) , discrete mathematics , combinatorics , mathematical analysis , invertible matrix , philosophy , physics , epistemology , artificial intelligence , computer science , acoustics
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.