Abstract
We start with summarizing some necessary auxiliary material from functional analysis and operator theory with special emphasis on local invertibility theories in Banach algebras. Then to give the reader a first idea of the usefulness of abstract local principles, we examine the so-called finite section method for Toeplitz operators. From this application we are finally going to extract a general scheme of using Banach algebra techniques which allows to tackle a lot of different invertibility problems (including the Fredholmness of Toeplitz and Wiener-Hopf operators and the stability of spline approximation methods for singular integral and Mellin operators) from a common point of view.
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© 1995 Birkhäuser Verlag
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Hagen, R., Roch, S., Silbermann, B. (1995). Invertibility in Banach algebras. In: Spectral Theory of Approximation Methods for Convolution Equations. Operator Theory Advances and Applications, vol 74. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9067-0_1
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DOI: https://doi.org/10.1007/978-3-0348-9067-0_1
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9891-1
Online ISBN: 978-3-0348-9067-0
eBook Packages: Springer Book Archive