Czechoslovak Mathematical Journal, first online, pp. 1-7


Some results on (strong) asymptotic Toeplitzness and Hankelness

Mehdi Nikpour

Received August 23, 2017.   Published online August 28, 2018.

Abstract:  Based on the results in A. Feintuch (1989), this work sheds light upon some interesting properties of strongly asymptotically Toeplitz and Hankel operators, and relations between these two classes of operators. Indeed, among other things, two main results here are (a) vanishing Toeplitz and Hankel operators forms an ideal, and (b) finding the distance of a strongly asymptotically Toeplitz operator from the set of vanishing Toeplitz operators.
Keywords:  Hardy space of the unit circle; Toeplitz operator; Hankel operator; strong operator topology
Classification MSC:  47B35, 47L80
DOI:  10.21136/CMJ.2018.0391-17

PDF available at:  Springer   Institute of Mathematics CAS

References:
[1] J. Barría, P. R. Halmos: Asymptotic Toeplitz operators. Trans. Amer. Math. Soc. 273 (1982), 621-630. DOI 10.2307/1999932 | MR 0667164 | Zbl 0522.47020
[2] A. Brown, P. R. Halmos: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213 (1963), 89-102. DOI 10.1515/crll.1964.213.89 | MR 0160136 | Zbl 0116.32501
[3] A. Feintuch: On asymptotic Toeplitz and Hankel operators. Oper. Theory, Adv. Appl. 41 (1989), 241-254. DOI 10.1007/978-3-0348-9278-0_12 | MR 1038338 | Zbl 0676.47014
[4] S. C. Power: Hankel Operators on Hilbert Space. Research Notes in Mathematics 64. Pitman Advanced Publishing Program, London (1982). MR 0666699 | Zbl 0489.47011

Affiliations:   Mehdi Nikpour, University of Colorado Denver, 1201 Larimer St., Denver, CO 80204, USA, e-mail: mehdi.nikpour@gmail.com


 
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