Necessary Condition for Vector-Valued Model Spaces to be Invariant Under Conjugation

The $S^{*}$-invariant subspaces of the Hardy-Hilbert space $H^{2}(E)$ (where $E$ is finite dimensional Hilbert space of dimension greater than 1) on the unit disc is well known. In this study, we examine that, if $\Omega$ is a conjugation on $E$, and $\Theta$ an inner function, then there exist model spaces which are not invariant for the conjugation $C_{\Omega}:L^{2}(E)\longrightarrow L^{2}(E)$. Under what necessary condition the model spaces is mapped onto itself is under consideration.

Keywords:

Inner function model spaces, conjugation,

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Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 2014
Yayıncı: Naim Çağman

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