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Reflexivity of Toeplitz operators in multiply connected regions

Wojciech Młocek;  Marek Ptak — 2016

Colloquium Mathematicae

Subspaces of Toeplitz operators on the Hardy spaces over a multiply connected region in the complex plane are investigated. A universal covering map of such a region and the group of automorphisms invariant with respect to the covering map connect the Hardy space on this multiply connected region with a certain subspace of the classical Hardy space on the disc. We also present some connections of Toeplitz operators on both spaces from the reflexivity point of view.

On the reflexivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane

Wojciech Młocek;  Marek Ptak — 2013

Czechoslovak Mathematical Journal

The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between L ∞ spaces on the unit circle and the real line...

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