Finite rank commutator of Toeplitz operators or Hankel operators. (English) Zbl 1161.47020
The authors provide equivalent conditions for the commutator of two Toeplitz operators or two Hankel operators on the Hardy space to have finite rank. They also deal with a modified version of the problem studied in [X. Chen, K. Guo, K. Izuchi and D. Zheng, J. Reine Angew. Math. 578, 1–48 (2005; Zbl 1090.47017)] – namely, when is the product of two Hankel opertors equal to a finite-rank perturbation of a Hankel opertor? It is shown that \(H_f H_g - H_h\) has finite rank if and only if both \(H_fH_g\) and \(H_h\) have finite rank.
Reviewer: Miyeon Kwon (Platteville, WI)
MSC:
47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
47B10 | Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.) |