[Settfa] Fwd: seminar

[Wieslaw Kubis]

Dear all,

This Tuesday we shall have a guest Marek Ptak, see the attached 
abstract. You will also receive an automatic announcement today or tomorrow.

All the best,

Wieslaw

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\bf{ \centerline{\large{Toeplitz kernels and $M_z$--commuting conjugations
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%\bf{ \centerline{\large{ and invariant subspaces }}
% \centerline{ Toeplitz operators  }}

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\bf{ \centerline{\large{by Marek Ptak }}}


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  \rm
\centerline{(University of Agriculture in Krak\'ow, Poland)}

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We study conjugations in $L^2(\mathbb{T})$ and their relation with kernels of Toeplitz operators on $H^2(\mathbb{T})$ 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  $M_z$ --commuting and $M_z$--conjugations leaving invariant model spaces to the Toeplitz kernels setting.



Joint work with P. Dymek, A. P\l aneta.

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