Geodesic
Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups
Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 721-737

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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.
Keywords: Toeplitz operator, Fredholm operator, Fredholm index, essential spectrum, ordered Abelian group. 
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     author = {A. R. Mirotin},
     title = {Fredholm and spectral properties of {Toeplitz} operators on $H^p$ spaces over ordered groups},
     journal = {Sbornik. Mathematics},
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     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_5_a5/}
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A. R. Mirotin. Fredholm and spectral properties of Toeplitz operators on $H^p$ spaces over ordered groups. Sbornik. Mathematics, Tome 202 (2011) no. 5, pp. 721-737. http://geodesic.mathdoc.fr/item/SM_2011_202_5_a5/