Gallardo-Gutiérrez, EA and Partington, JR orcid.org/0000-0002-6738-3216 (2024) Insights on the Cesàro operator: shift semigroups and invariant subspaces. Journal d'Analyse Mathematique, 152 (1). pp. 595-614. ISSN 0021-7670
Abstract
A closed subspace is invariant under the Cesaro operator C on the classical Hardy space H2(D) if and only if its orthogonal complement is invariant under the C0-semigroup of composition operators induced by the affine maps ϕt(z) = e−tz + 1 − e−t for t ≥ 0 and z ∈ D. The corresponding result also holds in the Hardy spaces Hp(D) for 1 < p < ∞. Moreover, in the Hilbert space setting, by linking the invariant subspaces of C to the lattice of the closed invariant subspaces of the standard right-shift semigroup acting on a particular weighted L2-space on the line, we exhibit a large class of non-trivial closed invariant subspaces and provide a complete characterization of the finite codimensional ones, establishing, in particular, the limits of such an approach towards describing the lattice of all invariant subspaces of C. Finally, we present a functional calculus argument which allows us to extend a recent result by Mashreghi, Ptak and Ross regarding the square root of C and discuss its invariant subspaces.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This item is protected by copyright. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution and reproduction in any medium, provided the appropriate credit is given to the original authors and the source, and a link is provided to the Creative Commons license, indicating if changes were made (https://creativecommons.org/licenses/by/4.0/). |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Oct 2022 10:58 |
Last Modified: | 08 Nov 2024 11:57 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s11854-023-0305-0 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:191858 |