Abstract
We completely classify all Toeplitz and Hankel operators which commute; namely, we prove that that a non-trivial Hankel operator and a non-trivial Toeplitz operator commute if and only if the Hankel operator has symbolzψ, where ψ is the symbol of the Toeplitz operator, and ψ is an affine function of the characteristic function of certain “anti-symmetric” sets of the unit circle.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. Brown, P. R. Halmos,Algebraic properties of Toeplitz Operators, J. Reigne Angew. Math.,213 (1963/1964), 89–102.
P. Hartman, A. Wintner,On the spectrum of Toeplitz matrices, Amer. J. Math.,72 (1950), 359–366.
Z. Nehari,On bounded bilinear forms. Ann. of Math.,65 (1957), 153–162.
S. Power,Hankel Operators on Hilbert Space, Bull. London Math. Soc.,12 (1980), 422–442.
S. Power, “Hankel Operators on Hilbert Space,” Pittman Publishing, Boston, 1982.
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.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Martínez-Avendaño, R.A. When do Toeplitz and Hankel operators commute?. Integr equ oper theory 37, 341–349 (2000). https://doi.org/10.1007/BF01194483
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01194483