Aproximation by invertible elements and the generalized E-stable rank for A(D)R and C(D)sym

• Autores: Raymond Mortini, Rudolf Rupp
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 109, Nº 1, 2011, págs. 114-132
• Idioma: inglés
• DOI: 10.7146/math.scand.a-15180
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• Resumen

  • We determine the generalized E-stable ranks for the real algebra, C(D)sym, of all complex valued continuous functions on the closed unit disk, symmetric to the real axis, and its subalgebra A(D)R of holomorphic functions. A characterization of those invertible functions in C(E) is given that can be uniformly approximated on E by invertibles in A(D)R. Finally, we compute the Bass and topological stable rank of C(K)sym for real symmetric compact planar sets K.