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The stable rank and connected stable rank for certain non self-adjoint Banach algebras. (English) Zbl 1221.46052

The author determines the topological and connected stable rank of triangular matrix algebras over a unital Banach algebra and of certain nest algebras.

MSC:

46H99 Topological algebras, normed rings and algebras, Banach algebras
19B10 Stable range conditions
46L99 Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
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Full Text: Euclid

References:

[1] K. R. Davidson, R. H. Levene, L. W. Marcoux, and H. Radjavi, On the topological stable rank of non-selfadjoint operator algebras , Math. Ann., 341 (2008), 239-253. · Zbl 1147.46030 · doi:10.1007/s00208-007-0180-5
[2] K. R. Davidson and Y. Q. Ji, Topological stable rank of nest algebras , Proc. London Math. Soc. (3), 98 (2009), 652-678. · Zbl 1178.47052 · doi:10.1112/plms/pdn048
[3] N. Elhage Hassan, Rangs stables de certaines extensions , J. London Math. Soc. (2), 52 (1995), 605-624. · Zbl 0857.46036 · doi:10.1112/jlms/52.3.605
[4] R. H. Herman and L. N. Vaserstein, The stable range of \(C^*\)-algebras , Invent. Math., 77 (1984), 553-555. · Zbl 0559.46025 · doi:10.1007/BF01388839
[5] M. A. Rieffel, Dimension and stable rank in the K-theory of \(C^*\)-algebras , Proc. London Math. Soc., 46 (1983), 301-333. · Zbl 0533.46046 · doi:10.1112/plms/s3-46.2.301
[6] M. A. Rieffel, The homotopy groups of the unitary groups of non-commutative tori , J. Operator Theory, 17 (1987), 237-254. · Zbl 0656.46056
[7] T. Sudo, The connected stable rank for Banach \(\ast\)-algebras involving isometries , Asian-European J. Math., 3 (2010), 185-191. · Zbl 1195.46051 · doi:10.1142/S179355711000012X
[8] N. E. Wegge-Olsen, K-theory and \(C^*\)-algebras , Oxford Univ. Press, 1993. · Zbl 0780.46038
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