Approximations of subhomogeneous algebras. (English) Zbl 1437.46056
Summary: Let \(n\) be a positive integer. A \(C^{\ast }\)-algebra is said to be \(n\)-subhomogeneous if all its irreducible representations have dimension at most \(n\). We give various approximation properties characterising \(n\)-subhomogeneous \(C^{\ast }\)-algebras.
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
| 46K10 | Representations of topological algebras with involution |
| 46L07 | Operator spaces and completely bounded maps |
| 47L30 | Abstract operator algebras on Hilbert spaces |
| 47L55 | Representations of (nonselfadjoint) operator algebras |
Keywords:
subhomogeneous algebra; \(C^\ast\)-algebra; finite-dimensional algebra; completely positive map; completely contractive mapReferences:
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