On the stable rank and reducibility in algebras of real symmetric functions |
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| Authors: | R Rupp A Sasane |
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| Institution: | 1. Fakult?t Allgemeinwissenschaften, Georg‐Simon‐Ohm‐Hochschule Nürnberg, Ke?lerplatz 12, 90489 Nürnberg, Germany;2. Phone: +49911 58801741, Fax: +49911 58805800;3. Department of Mathematics, Royal Institute of Technology, 100 44 Stockholm, Sweden |
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| Abstract: | Let A?(??) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that A?(??) 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 condition for reducibility in some real algebras of functions on symmetric domains with holes, which is a generalization of the main theorem in 18]. A sufficient topological condition on the symmetric open set ?? is given for the corresponding real algebra A?(??) to have Bass stable rank equal to 1 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Real Banach algebras Bass stable rank topological stable rank reducibility stabilization |
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