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Concrete Operators

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Invertible and normal composition operators on the Hilbert Hardy space of a half–plane

Valentin Matache
Published Online: 2016-05-16 | DOI: https://doi.org/10.1515/conop-2016-0009


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.

Keywords: Composition operator; Hardy space; Half–plane


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About the article

Received: 2015-10-09

Accepted: 2016-04-27

Published Online: 2016-05-16

Citation Information: Concrete Operators, Volume 3, Issue 1, Pages 77–84, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2016-0009.

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© 2016 Valentin Matache. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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