International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 96289, 7 pages
Joint Spectra of Generators in Topological Algebras
Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenue San Rafael Atlixco 186, Col. Vicentina, AP 55-534, México 09340, DF, Mexico
Received 29 October 2006; Revised 24 January 2007; Accepted 8 February 2007
Academic Editor: Ricardo Estrada
Copyright © 2007 Antoni Wawrzyńczyk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a complex topological algebra with unit 1 and a
family of proper closed ideals in . For an arbitrary
we define a globally defined joint spectrum
. We prove that for generating the spectrum can be identified with the set of
continuous multiplicative functionals on such that ker . The relation is given by the formula
. If is a -algebra, the set is rationally convex.