Hermitian composition operators on Hardy-Smirnov spaces

Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian compositi...

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Main Author: Gunatillake Gajath
Format: Article
Language:English
Published: De Gruyter 2017-01-01
Series:Concrete Operators
Subjects:
Online Access:https://doi.org/10.1515/conop-2017-0002
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author Gunatillake Gajath
author_facet Gunatillake Gajath
author_sort Gunatillake Gajath
collection DOAJ
description Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
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spelling doaj.art-e54703caa4fd410fb503ab87f56e14302022-12-21T19:14:09ZengDe GruyterConcrete Operators2299-32822017-01-014171710.1515/conop-2017-0002conop-2017-0002Hermitian composition operators on Hardy-Smirnov spacesGunatillake Gajath0American University of Sharjah, Sharjah, United Arab EmiratesLet Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f º φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.https://doi.org/10.1515/conop-2017-0002composition operatorhermitian operatorhardy-smirnov space47b3330h10
spellingShingle Gunatillake Gajath
Hermitian composition operators on Hardy-Smirnov spaces
Concrete Operators
composition operator
hermitian operator
hardy-smirnov space
47b33
30h10
title Hermitian composition operators on Hardy-Smirnov spaces
title_full Hermitian composition operators on Hardy-Smirnov spaces
title_fullStr Hermitian composition operators on Hardy-Smirnov spaces
title_full_unstemmed Hermitian composition operators on Hardy-Smirnov spaces
title_short Hermitian composition operators on Hardy-Smirnov spaces
title_sort hermitian composition operators on hardy smirnov spaces
topic composition operator
hermitian operator
hardy-smirnov space
47b33
30h10
url https://doi.org/10.1515/conop-2017-0002
work_keys_str_mv AT gunatillakegajath hermitiancompositionoperatorsonhardysmirnovspaces