The essential spectrum of some Toeplitz operators

Clancey, Kevin F.; Morrel, Bernard B.

doi:10.1090/S0002-9939-1974-0341162-9

The essential spectrum of some Toeplitz operators
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by Kevin F. Clancey and Bernard B. Morrel

Proc. Amer. Math. Soc. 44 (1974), 129-134

DOI: https://doi.org/10.1090/S0002-9939-1974-0341162-9

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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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