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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Asymptotic Toeplitz operators


Authors: José Barría and P. R. Halmos
Journal: Trans. Amer. Math. Soc. 273 (1982), 621-630
MSC: Primary 47B35
DOI: https://doi.org/10.1090/S0002-9947-1982-0667164-X
MathSciNet review: 667164
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Abstract: An asymptotic Toeplitz is an operator $ T$ such the sequence $ \{ {U^{ \ast n}}T{U^n}\} $ is strongly convergent, where $ U$ is the unilateral shift. Every element of the norm-closed algebra generated by all Toeplitz and Hankel opertors together is an asymptotic Toeplitz operator. The authors study the relations among this Hankel algebra, the classical Toeplitz algebra, the set of all asymptotic Toeplitz operators, and the essential commutant of the unilateral shift. They offer several examples of operators in some of these classes but not in others, and they raise several open questions.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0667164-X
Article copyright: © Copyright 1982 American Mathematical Society