Complex symmetric composition operators on the Newton space

Han, Kaikai

doi:10.1016/j.jmaa.2020.124091

Cited by 8 publications

(2 citation statements)

References 19 publications

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“…Using the same rule as J, but in other spaces, [19,20,21,23] also described weighted composition operators and composition operators that are J-symmetric.…”

Section: Complex Symmetric Composition Operatorsmentioning

confidence: 99%

“…They have also shown that constant self-maps of U and involutive disc automorphisms induce non-normal complex symmetric composition operators on H 2 (U). Since then, several authors have been interested in the subject, describing complex symmetric composition operators and exhibiting concrete conjugations for which C Φ is complex symmetric (see [2,19,21,27]). Results on how the complex symmetry of C Φ affects the analytic self-map Φ were obtained in [2,11].…”

Section: Introductionmentioning

confidence: 99%

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Composition operators on Hardy-Smirnov spaces

V.¹,

V.²,

Pellegrino³

et al. 2021

Preprint

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We investigate composition operators CΦ on the Hardy-Smirnov space H 2 (Ω) induced by analytic self-maps Φ of an open simply connected proper subset Ω of the complex plane. When the Riemann map τ : U → Ω used to define the norm of H 2 (Ω) is a linear fractional transformation, we characterize the composition operators whose adjoints are composition operators. As applications of this fact, we provide a new proof for the adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodríguez and we give a new approach to describe all Hermitian and unitary composition operators on H 2 (Ω). Additionally, if the coefficients of τ are real, we exhibit concrete examples of conjugations and describe the Hermitian and unitary composition operators which are complex symmetric with respect to specific conjugations on H 2 (Ω). We finish this paper showing that if Ω is unbounded and Φ is a non-automorphic self-map of Ω with a fixed point, then CΦ is never complex symmetric on H 2 (Ω).

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“…Using the same rule as J, but in other spaces, [19,20,21,23] also described weighted composition operators and composition operators that are J-symmetric.…”

Section: Complex Symmetric Composition Operatorsmentioning

confidence: 99%