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Concrete Operators

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An introduction to Rota’s universal operators: properties, old and new examples and future issues

Carl C. Cowen / Eva A. Gallardo-Gutiérrez
  • Corresponding author
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid e ICMAT, Plaza de Ciencias 3, 28040, Madrid, Spain
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Published Online: 2016-04-14 | DOI: https://doi.org/10.1515/conop-2016-0006


The Invariant Subspace Problem for Hilbert spaces is a long-standing question and the use of universal operators in the sense of Rota has been an important tool for studying such important problem. In this survey, we focus on Rota’s universal operators, pointing out their main properties and exhibiting some old and recent examples.

Keywords: Rota’s universal operators; Invariant subspace; Analytic Toeplitz operator; Lomonosov’s Theorem


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About the article

Received: 2015-12-03

Accepted: 2016-01-26

Published Online: 2016-04-14

Citation Information: Concrete Operators, Volume 3, Issue 1, Pages 43–51, ISSN (Online) 2299-3282, DOI: https://doi.org/10.1515/conop-2016-0006.

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© 2016 Cowen and Gallardo-Gutiérrez. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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