Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups

A. R. Mirotin

Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 721-737

Résumé

We consider Toeplitz operators on the spaces $H^p(G)$, $1< p<\infty$, associated with a compact connected Abelian group $G$ whose character group is ordered and, in the case of total order, prove a theorem on the Fredholm index for those operators which have continuous symbols which generalizes the classical Gohberg-Krein theorem. The results thus obtained are applied to the spectral theory of Toeplitz operators and examples where the index is evaluated explicitly are considered. Bibliography: 22 titles.

Détail

Keywords: Toeplitz operator, Fredholm operator, Fredholm index, essential spectrum, ordered Abelian group.

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