Spectrum, similarity, and invariant subspaces of Toeplitz operators

V. V. Peller

Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 133-144.

Résumé

Estimates are obtained for the resolvents of Toeplitz operators under certain restrictions on their symbols. Conditions are found for the existence of nontrivial invariant subspaces and for a Toeplitz operator to be similar to a unitary operator. A theorem on inclusion of spectra is obtained for Toeplitz operators with unimodular symbols. Bibliography: 26 titles.

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