**
J. Rákosník (ed.), **

Function spaces, differential operators and nonlinear analysis.

Proceedings of the conference held in Paseky na Jizerou, September 3-9, 1995.

Mathematical Institute, Czech Academy of Sciences, and Prometheus Publishing House, Praha 1996

p. 101 - 112

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Spectral invariance for pseudodifferential operators on function spaces

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Hans-Gerd Leopold

Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich-Schiller-Universität, Leutragraben 1, 07743 Jena, Germany leopold@minet.uni-jena.de

**Abstract:** In joint papers with E. Schrohe and H. Triebel the relations between invertibility in the algebra of pseudodifferential operators and invertibility in the operator theoretical sense with respect to different function spaces were discussed. As a consequence it was shown, that for a large class of pseudodifferential operators, acting on function spaces of Besov-Triebel-Lizorkin type with and without weights, the spectrum is independent of the choice of space-parameters and coincides with its $L_2$ spectrum.

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