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When do Toeplitz and Hankel operators commute? (English) Zbl 0961.47015
The author shows that non-trivial Toeplitz ($$T_\psi$$) and Hankel ($$H_\varphi$$) operators commute if and only if the symbol $$\varphi$$ of Hankel operator is $$z\psi (z)$$, where $$\psi(z)=a\xi (z)+b$$, $$a\neq 0$$ and $$\xi (z)$$ is the characteristic function of certain “anti-symmetric” sets of the unit circle.

##### MSC:
 47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
##### Keywords:
Toeplitz operator; Hankel operator; symbol
Full Text:
##### References:
 [1] A. Brown, P. R. Halmos,Algebraic properties of Toeplitz Operators, J. Reigne Angew. Math.,213 (1963/1964), 89-102. · Zbl 0116.32501 [2] P. Hartman, A. Wintner,On the spectrum of Toeplitz matrices, Amer. J. Math.,72 (1950), 359-366. · Zbl 0035.35903 [3] Z. Nehari,On bounded bilinear forms. Ann. of Math.,65 (1957), 153-162. · Zbl 0077.10605 [4] S. Power,Hankel Operators on Hilbert Space, Bull. London Math. Soc.,12 (1980), 422-442. · Zbl 0446.47015 [5] S. Power, ?Hankel Operators on Hilbert Space,? Pittman Publishing, Boston, 1982. [6] D. Sarason,Holomorphic spaces: a brief and selective survey, in ?Holomorphic Spaces (Berkeley), CA, 1995)?, 1-34, Math. Sci. Res. Inst. Publ. 33, Cambridge Univ. Press, Cambridge, 1998. · Zbl 1128.47312
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