Conjugations in $$L^2(\mathcal {H})$$
AbstractConjugations commuting with $$\mathbf {M}_z$$ M z and intertwining $$\mathbf {M}_z$$ M z and $$\mathbf {M}_{{\bar{z}}}$$ M z ¯ in $$L^2(\mathcal {H})$$ L 2 ( H ) , where $$\mathcal {H}$$ H is a separable Hilbert space, are characterized. We also investigate which of them leave invariant the whole Hardy space $$H^2(\mathcal {H})$$ H 2 ( H ) or a model space $$K_\Theta =H^2(\mathcal {H})\ominus \Theta H^2(\mathcal {H})$$ K Θ = H 2 ( H ) ⊖ Θ H 2 ( H ) , where $$\Theta $$ Θ is a pure operator valued inner function.
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1982 ◽
Vol 34
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pp. 1245-1250
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1974 ◽
Vol 26
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pp. 565-575
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Vol 25
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