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Brownian Type Parts of Operators in Hilbert Spaces

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Abstract

We obtain some reducing (or just invariant) subspaces for a Hilbert space operator on which it acts as a Brownian type 2-isometry. More exactly Brownian isometric (unitary) parts as well as more general quasi-Brownian isometric (unitary) parts of an operator are investigated. They are explicitely described for a 2-isometry.

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Acknowledgements

The authors are grateful to the referee for careful reading of the paper and valuable comments. Part of the research was carried out during the visits of the second author to the AGH University of Krakow in July 2018 and May–June 2019. He is grateful to his hosts for their hospitality and support. The second author was also supported by a project financed by Lucian Blaga University of Sibiu and Hasso Plattner Foundation research Grants LBUS-IRG-2019-05.

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Authors and Affiliations

  1. Faculty of Applied Mathematics, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059, Kraków, Poland

    Witold Majdak

  2. Department of Mathematics and Informatics, “Lucian Blaga” University of Sibiu, Sibiu, Romania

    Laurian Suciu

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  1. Witold Majdak
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  2. Laurian Suciu
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Correspondence to Laurian Suciu.

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Majdak, W., Suciu, L. Brownian Type Parts of Operators in Hilbert Spaces. Results Math 75, 5 (2020). https://doi.org/10.1007/s00025-019-1130-8

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  • DOI: https://doi.org/10.1007/s00025-019-1130-8

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