Abstract
We consider Toeplitz operators on the spaces , , associated with a compact connected Abelian group 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.
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