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arXiv · 1207.1269

Norm-Controlled Inversion in Smooth Banach Algebras, I

Karlheinz Gröchenig·Andreas Klotz
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Abstract

Every differential subalgebra of a unital $C^*$-algebra is spectrally invariant. We derive a quantitative version of this well-known fact and show that a minimal amount of smoothness, as given by a differential norm, already implies norm control. We obtain an explicit estimate for the differential norm of an invertible element $a$. This estimate depends only on the condition number of $a$ and the ratio of two norms.

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Karlheinz Gröchenig, Andreas Klotz. 2012-07-05. Norm-Controlled Inversion in Smooth Banach Algebras, I. https://doi.org/10.1112/jlms%2Fjdt004

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