Rupp, R. and Sasane, Amol (2010) On the stable rank and reducibility in algebras of real symmetric functions. Mathematische nachrichten, 283 (8). pp. 1194-1206. ISSN 0025-584X
Let Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) has Bass and topological stable ranks equal to 2, which settles the conjecture made by Brett Wick in . 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 . A sufficient topological condition on the symmetric open set [MATHEMATICAL DOUBLE-STRUCK CAPITAL D] is given for the corresponding real algebra Aℝ([MATHEMATICAL DOUBLE-STRUCK CAPITAL D]) to have Bass stable rank equal to 1.
|Additional Information:||© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim|
|Uncontrolled Keywords:||Real Banach algebras, bass stable rank, topological stable rank, reducibility, stabilization|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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