Approximately finitely acting operator algebras.

Power, Stephen C. (2002) Approximately finitely acting operator algebras. Journal of Functional Analysis, 189 (2). pp. 409-468. ISSN 0022-1236

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Let E be an operator algebra on a Hilbert space with finite-dimensional C*-algebra C*(E). A classification is given of the locally finite algebras A0=[formula](Ak, φk) and the operator algebras A=[formula](Ak, φk) obtained as limits of direct sums of matrix algebras over E with respect to star-extendible homomorphisms. The invariants in the algebraic case consist of an additive semigroup, with scale, which is a right module for the semiring VE=Homu(E, E) of unitary equivalence classes of star-extendible homomorphisms. This semigroup is referred to as the dimension module invariant. In the operator algebra case the invariants consist of a metrized additive semigroup with scale and a contractive right module VE-action. Subcategories of algebras determined by restricted classes of embeddings, such as 1-decomposable embeddings between digraph algebras, are also classified in terms of simplified dimension modules.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Functional Analysis
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RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics
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Deposited On:
01 Apr 2008 12:53
Last Modified:
21 Nov 2022 19:13