Approximation by invertible elements and the generalized E-stable rank for A({\boldsymbol D})_{\mathsf R} and C({\boldsymbol D})_{\mathrm{sym}}
DOI:
https://doi.org/10.7146/math.scand.a-15180Abstract
We determine the generalized E-stable ranks for the real algebra, C(\boldsymbol{D})_{\mathrm{sym}}, of all complex valued continuous functions on the closed unit disk, symmetric to the real axis, and its subalgebra A(\boldsymbol{D})_{\mathsf 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(\boldsymbol {D})_{\mathsf R}. Finally, we compute the Bass and topological stable rank of C(K)_{\mathrm{sym}} for real symmetric compact planar sets K.Downloads
Published
2011-09-01
How to Cite
Mortini, R., & Rupp, R. (2011). Approximation by invertible elements and the generalized E-stable rank for A({\boldsymbol D})_{\mathsf R} and C({\boldsymbol D})_{\mathrm{sym}}. MATHEMATICA SCANDINAVICA, 109(1), 114–132. https://doi.org/10.7146/math.scand.a-15180
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