Inverse Closed Ultradifferential Subalgebras
Functional Analysis
2012-01-17 v1 Operator Algebras
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.
Keywords
Cite
@article{arxiv.1201.2938,
title = {Inverse Closed Ultradifferential Subalgebras},
author = {Andreas Klotz},
journal= {arXiv preprint arXiv:1201.2938},
year = {2012}
}