Compact products of Toeplitz operators on the Dirichlet space of the unit ball. (English) Zbl 1303.47040
Authors’ abstract: We consider, on the Dirichlet space of the unit ball, operators which have the form of a finite sum of products of several Toeplitz operators and then give a characterization for which such an operator is compact. We show, as an application, that for \(n\geq 2\), there is no nontrivial compact product of several Toeplitz operators with pluriharmonics symbols, which is a higher dimensional phenomenon whose one-variable analogue is false.
Reviewer: Pengyan Hu (Shenzhen)
MSC:
47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |
32A37 | Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA)) |
46E15 | Banach spaces of continuous, differentiable or analytic functions |
47B38 | Linear operators on function spaces (general) |