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Keywords:
Hardy space of the unit circle; Toeplitz operator; Hankel operator; strong operator topology
Hardy space of the unit circle; Toeplitz operator; Hankel operator; strong operator topology
Summary:
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.
References:
[1] Barría, J., Halmos, P. R.: Asymptotic Toeplitz operators. Trans. Amer. Math. Soc. 273 (1982), 621-630. DOI 10.2307/1999932 | MR 0667164 | Zbl 0522.47020
[2] Brown, A., Halmos, P. R.: 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] Feintuch, A.: 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] Power, S. C.: Hankel Operators on Hilbert Space. Research Notes in Mathematics 64. Pitman Advanced Publishing Program, London (1982). MR 0666699 | Zbl 0489.47011
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