Conjugations on $$\varvec{L^2(\mathbb {T}^N)}$$ L 2 ( T N ) and Invariant Subspaces

Piotr Dymek (), Artur Płaneta () and Marek Ptak ()
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Piotr Dymek: Katedra Zastosowa´n Matematyki, Uniwersytet Rolniczy w Krakowie
Artur Płaneta: Katedra Zastosowa´n Matematyki, Uniwersytet Rolniczy w Krakowie
Marek Ptak: Katedra Zastosowa´n Matematyki, Uniwersytet Rolniczy w Krakowie

A chapter in Multivariable Operator Theory, 2023, pp 407-418 from Springer

Abstract: Abstract We study conjugations on $$L^2(\mathbb {T}^N)$$ L 2 ( T N ) and their behaviour with respect to multiplication operators. Full characterizations of conjugations commuting or intertwining with multiplication operators are obtained. We also characterize conjugations leaving invariant subspaces being invariant for multiplication by independent variables. The subspaces not being the multiplication of the Hardy space $$H^2(\mathbb {D}^N)$$ H 2 ( D N ) by inner function are also considered.

Keywords: Conjugation; Invariant subspaces; Unimodular functions; Symmetric functions; Hardy space on a polydisc; Primary 47A13; Secondary 47A15; 47B91 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/978-3-031-50535-5_15

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