Power, Stephen C. (2002) Approximately finitely acting operator algebras. Journal of Functional Analysis, 189 (2). pp. 409-468. ISSN 0022-1236Full text not available from this repository.
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.
|Journal or Publication Title:||Journal of Functional Analysis|
|Additional Information:||RAE_import_type : Journal article RAE_uoa_type : Pure Mathematics|
|Uncontrolled Keywords:||operator algebra ; approximately finite ; nonselfadjoint ; classification ; metrized semiring|
|Subjects:||Q Science > QA Mathematics|
|Departments:||Faculty of Science and Technology > Mathematics and Statistics|
|Deposited On:||01 Apr 2008 13:53|
|Last Modified:||07 Jan 2015 13:48|
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