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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The essential spectrum of some Toeplitz operators

Authors: Kevin F. Clancey and Bernard B. Morrel
Journal: Proc. Amer. Math. Soc. 44 (1974), 129-134
MSC: Primary 47B35
MathSciNet review: 0341162
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Abstract: The localization techniques of Douglas and Sarason are used to obtain the essential spectrum of the Toeplitz operator $ {T_\varphi }$ for which $ \varphi $ is the product of a continuous function and the characteristic function of a measurable subset of the unit circle. Examples are given of Toeplitz operators with one-dimensional self-commutator whose essential spectrum is the unit disk. Using an example of J. E. Brennan, the authors show the existence of a completely nonnormal, subnormal operator whose adjoint has no point spectrum.

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Keywords: Hyponormal operator, Toeplitz operator, essential spectrum
Article copyright: © Copyright 1974 American Mathematical Society