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Proceedings of the American Mathematical Society

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

 

 

The numerical range of a Toeplitz operator


Author: E. M. Klein
Journal: Proc. Amer. Math. Soc. 35 (1972), 101-103
MSC: Primary 47B35
DOI: https://doi.org/10.1090/S0002-9939-1972-0296725-4
MathSciNet review: 0296725
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Abstract: In this paper we explicitly compute the numerical range of an arbitrary Toeplitz operator on the classical Hardy space $ {H^2}$ of the unit circle. In particular, we show that the numerical range depends only on the spectrum of the given Toeplitz operator. Several special cases are also considered.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0296725-4
Keywords: Toeplitz operator, numerical range, spectrum, convexoid operator
Article copyright: © Copyright 1972 American Mathematical Society