1987•Mathematics of the USSR-IzvestiyaRequires access

SPECTRUM, SIMILARITY, AND INVARIANT SUBSPACES OF TOEPLITZ OPERATORS

Vladimir Vsevolodovich Peller

Abstract

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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Key concepts: Toeplitz matrix, Linear subspace, Invariant (physics), Mathematics, Similarity (geometry), Pure mathematics, Reflexive operator algebra, Pattern recognition (psychology)