JournalszaaVol. 8, No. 4pp. 293–306

A. Symbol Calculus for the Algebra Generated by Shift Operators

  • Steffen Roch

    Technische Hochschule Darmstadt, Germany

  • Bernd Silbermann

    Technische Universität Chemnitz, Germany
A. Symbol Calculus for the Algebra Generated by Shift Operators cover
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Abstract

We describe the algebraical structure of the algebra generated by the shift operator and by one of its left-inverses and construct a symbol for the invertibility of an operator modulo the quasicommutator ideal. The correspondence between this symbol and the invertibility and Fredholmness of elements of this algebra are studied.

Cite this article

Steffen Roch, Bernd Silbermann, A. Symbol Calculus for the Algebra Generated by Shift Operators. Z. Anal. Anwend. 8 (1989), no. 4, pp. 293–306

DOI 10.4171/ZAA/355