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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Format: | Article |
Language: | English |
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De Gruyter
2017-01-01
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Series: | Concrete Operators |
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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. |
first_indexed | 2024-12-21T05:45:15Z |
format | Article |
id | doaj.art-e54703caa4fd410fb503ab87f56e1430 |
institution | Directory Open Access Journal |
issn | 2299-3282 |
language | English |
last_indexed | 2024-12-21T05:45:15Z |
publishDate | 2017-01-01 |
publisher | De Gruyter |
record_format | Article |
series | Concrete Operators |
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 |