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 |
| Summary: | 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. |
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| ISSN: | 2299-3282 |