Stable rank of \(C^*\)-algebras of type I. (English) Zbl 1049.46043
Summary: In this paper, we estimate the stable rank and connected stable rank of \(C^*\)-algebras under a technical assumption on their spectra. Using this result, we obtain some stable rank formulas for type I \(C^*\)-algebras. In particular, we obtain a product formula for the stable rank of type I \(C^*\)-algebras.
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 19K56 | Index theory |
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