Images of Hankel operators on the polydisk

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.

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...

Hankel Operators on Hilbert Space

commonly known as Hilbert's matrix, determines a bounded linear operator on the Hilbert space of square summable complex sequences. Infinite matrices which possess a similar form to H, namely those that are 'one way infinite' and have identical entries in cross diagonals, are called Hankel matrices, and when these matrices determine bounded operators we have Hankel operators, the subject of thi...

Intermediate Hankel Operators on the Bergman Space

On Truncations of Hankel and Toeplitz Operators

We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes. 1. Statement of results In this note we will be dealing with infinite ma...