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

Abstract

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 we redefine the classical isomorphism between L1 spaces.