Geodesic
Some results on (strong) asymptotic Toeplitzness and Hankelness
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 471-477
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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.
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.
DOI : 10.21136/CMJ.2018.0391-17
Classification : 47B35, 47L80
Keywords: Hardy space of the unit circle; Toeplitz operator; Hankel operator; strong operator topology 
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Nikpour, Mehdi. Some results on (strong) asymptotic Toeplitzness and Hankelness. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 2, pp. 471-477. doi: 10.21136/CMJ.2018.0391-17

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[2] Brown, A., Halmos, P. R.: Algebraic properties of Toeplitz operators. J. Reine Angew. Math. 213 (1963), 89-102. | DOI | MR | JFM

[3] Feintuch, A.: On asymptotic Toeplitz and Hankel operators. Oper. Theory, Adv. Appl. 41 (1989), 241-254. | DOI | MR | JFM

[4] Power, S. C.: Hankel Operators on Hilbert Space. Research Notes in Mathematics 64. Pitman Advanced Publishing Program, London (1982). | MR | JFM

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