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

## Abstract

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: | Article |
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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 |

ID Code: | 2386 |

Deposited By: | ep_importer |

Deposited On: | 01 Apr 2008 13:53 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 04 Apr 2016 01:06 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/2386 |

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