Toeplitz operators on the polydisk

Algebraic Properties of Toeplitz Operators on the Polydisk

and Applied Analysis 3 For commuting problem, in 1963, Brown and Halmos 2 showed that two bounded Toeplitz operators Tφ and Tψ on the classical Hardy space commute if and only if i both φ and ψ are analytic, ii both φ and ψ are analytic, or iii one is a linear function of the other. On the Bergman space of the unit disk, some similar results were obtained for Toeplitz operators with bounded har...

The Numerical Range of Toeplitz Operator on the Polydisk

and Applied Analysis 3 It is obvious that ka ∈ A2 D and 〈ka, ka〉 ∫

On Weighted Toeplitz Operators

A weighted Toeplitz operator on H(β) is defined as Tφf = P (φf) where P is the projection from L(β) onto H(β) and the symbol φ ∈ L(β) for a given sequence β = 〈βn〉n∈Z of positive numbers. In this paper, a matrix characterization of a weighted multiplication operator on L(β) is given and it is used to deduce the same for a weighted Toeplitz operator. The eigenvalues of some weighted Toeplitz ope...

Compact Hankel Operators on the Hardy Space of the Polydisk

We show that a big Hankel operator on the standard Hardy space of the polydisk D, n > 1, cannot be compact unless it is the zero operator. We also show that this result can be generalized to certain Hankel operators defined on Hardy-Sobolev spaces of the polydisk.

Toeplitz Operators on Fock Spaces