Inverse closed ultradifferential subalgebras |
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Authors: | Andreas Klotz |
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Institution: | Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, A-1090 Vienna, Austria |
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Abstract: | In previous work we have shown that classical approximation theory provides methods for the systematic construction of inverse-closed smooth subalgebras. Now we extend this work to treat inverse-closed subalgebras of ultradifferentiable elements. In particular, Carleman classes and Dales–Davie algebras are treated. As an application the result of Demko, Smith and Moss, and Jaffard on the inverse of a matrix with exponential decay is obtained within the framework of a general theory of smoothness. |
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Keywords: | Banach algebra Inverse closedness Spectral invariance Carleman classes Dales&ndash Davie algebras Matrix algebra Off-diagonal decay Automorphism group |
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