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Stable ranks of split extensions of Banach algebras

✍ Scribed by You Qing Ji; Yuan Hang Zhang

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 238 KB
Volume: 434
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.12.009

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✦ Synopsis

In this paper, we estimate the stable ranks of a Banach algebra in terms of the stable ranks of its quotient algebra and ideal under the assumption that the quotient map splits. As an application, several results about the Bass and the connected stable ranks of nest algebras are obtained.

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## Abstract Let __A__~ℝ~(𝔻) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that __A__~ℝ~(𝔻) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in [18]. We also give a necessary and sufficient conditi