Conjugations Preserving Toeplitz Kernels

Abstract

AbstractWe study conjugations in $$L^2(\mathbb {T})$$ L 2 ( T ) and their relation with kernels of Toeplitz operators on $$H^2(\mathbb {T})$$ H 2 ( T ) space. Such kernels are a generalization of model spaces. We investigate properties of an inequality relation between two unimodular functions defined on the unit circle. This allows us to significantly strengthen previous theorems characterizing all $$M_z$$ M z -commuting and $$M_z$$ M z -conjugations leaving invariant model spaces to the Toeplitz kernels setting.