Invertible and normal composition operators on the Hilbert Hardy space of a half–plane
Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We...
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| Format: | Article |
| Language: | English |
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De Gruyter
2016-05-01
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| Series: | Concrete Operators |
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| Online Access: | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0009/conop-2016-0009.xml?format=INT |
| _version_ | 1818192526520090624 |
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| author | Matache Valentin |
| author_facet | Matache Valentin |
| author_sort | Matache Valentin |
| collection | DOAJ |
| description | Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition
operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and
characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal
composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra,
essential spectra, and numerical ranges. |
| first_indexed | 2024-12-12T00:31:54Z |
| format | Article |
| id | doaj.art-292bce9640d54c0dab9adf8b9347cfa2 |
| institution | Directory Open Access Journal |
| issn | 2299-3282 |
| language | English |
| last_indexed | 2024-12-12T00:31:54Z |
| publishDate | 2016-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Concrete Operators |
| spelling | doaj.art-292bce9640d54c0dab9adf8b9347cfa22022-12-22T00:44:27ZengDe GruyterConcrete Operators2299-32822016-05-0131778410.1515/conop-2016-0009conop-2016-0009Invertible and normal composition operators on the Hilbert Hardy space of a half–planeMatache Valentin0Department of Mathematics, University of Nebraska, Omaha, NE 68182, USAOperators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0009/conop-2016-0009.xml?format=INTComposition operator Hardy space Half–plane |
| spellingShingle | Matache Valentin Invertible and normal composition operators on the Hilbert Hardy space of a half–plane Concrete Operators Composition operator Hardy space Half–plane |
| title | Invertible and normal composition operators
on the Hilbert Hardy space of a half–plane |
| title_full | Invertible and normal composition operators
on the Hilbert Hardy space of a half–plane |
| title_fullStr | Invertible and normal composition operators
on the Hilbert Hardy space of a half–plane |
| title_full_unstemmed | Invertible and normal composition operators
on the Hilbert Hardy space of a half–plane |
| title_short | Invertible and normal composition operators
on the Hilbert Hardy space of a half–plane |
| title_sort | invertible and normal composition operators on the hilbert hardy space of a half plane |
| topic | Composition operator Hardy space Half–plane |
| url | http://www.degruyter.com/view/j/conop.2016.3.issue-1/conop-2016-0009/conop-2016-0009.xml?format=INT |
| work_keys_str_mv | AT matachevalentin invertibleandnormalcompositionoperatorsonthehilberthardyspaceofahalfplane |