Gallardo-Gutiérrez, EA, Partington, JR orcid.org/0000-0002-6738-3216 and Rodríguez, DJ (2016) A continuous model for quasinilpotent operators. Mathematische Zeitschrift, 284 (3-4). pp. 781-790. ISSN 0025-5874
Abstract
A classical result due to Foias and Pearcy establishes a discrete model
for every quasinilpotent operator acting on a separable, in nite-dimensional complex Hilbert space H. More precisely, given a quasinilpotent operator T on H, there exists a compact quasinilpotent operator K in H such that T is similar to a part of K ⊕K ⊕···⊕K ⊕··· acting on the direct sum of countably many copies of H. We show that a continuous model for any quasinilpotent operator can be provided. The consequences of such a model will be discussed in the context of C0-semigroups of quasinilpotent operators.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2016. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
Keywords: | Quasinilpotent operators; C0-semigroup; Operator model; Entire function |
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: | 14 Apr 2016 11:34 |
Last Modified: | 08 Sep 2020 16:59 |
Published Version: | https://doi.org/10.1007/s00209-016-1673-2 |
Status: | Published |
Publisher: | Springer Verlag |
Identification Number: | 10.1007/s00209-016-1673-2 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:98456 |