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

Authors : Rewayat KHAN, Jamroz KHAN

Pages : 1-4

View : 48 | Download : 12

Publication Date : 2019-05-07

Article Type : Research Paper

Abstract :The $S^{*}$-invariant subspaces of the Hardy-Hilbert space $H^{2}insert ignore into journalissuearticles values(E);$ insert ignore into journalissuearticles values(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 $C_{\Omega}:L^{2}insert ignore into journalissuearticles values(E);\longrightarrow L^{2}insert ignore into journalissuearticles values(E);$. Under what necessary condition the model spaces is mapped onto itself is under consideration.
Keywords : Inner function, model spaces, conjugation

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