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 such the sequence is strongly convergent, where 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