On the stable rank and reducibility in algebras of real symmetric functions
2010 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 283, no 8, 1194-1206 p.Article in journal (Refereed) Published
Let A(R) ((D) over bar) denote the set of functions belonging to the disc algebra having real Fourier coefficients. We show that A(R) ((D) over bar) 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 D is given for the corresponding real algebra A(R) ((D) over bar) to have Bass stable rank equal to 1. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Place, publisher, year, edition, pages
2010. Vol. 283, no 8, 1194-1206 p.
Real Banach algebras, Bass stable rank, topological stable rank, reducibility, stabilization
IdentifiersURN: urn:nbn:se:kth:diva-26845DOI: 10.1002/mana.200710080ISI: 000281068000007ScopusID: 2-s2.0-77956284113OAI: oai:DiVA.org:kth-26845DiVA: diva2:374579
QC 201012062010-12-062010-11-292010-12-06Bibliographically approved