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Quasiaffine transforms of Hilbert space operators

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Abstract

Ampliation quasisimilarity was applied as a tool in Foias and Pearcy (J Funct Anal 219:134–142, 2005) to reduce the hyperinvariant subspace problem to a particular class of operators. The seemingly weaker pluquasisimilarity relation was introduced in Bercovici et al. (Acta Sci Math Szeged 85:681–691, 2019) and studied also in Kérchy (Acta Sci Math Szeged 86:503–520, 2020). The problem whether these two relations are actually equivalent is addressed in the present paper. The following more general, related question is studied in details: under what conditions is the operator A a quasiaffine transform of B, whenever A can be injected into B and A can be also densely mapped into B.

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Authors and Affiliations

  1. St. Petersburg Branch, V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, Fontanka 27, Saint Petersburg, Russia, 191023

    Maria F. Gamal’

  2. Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, Szeged, 6720, Hungary

    László Kérchy

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  1. Maria F. Gamal’
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  2. László Kérchy
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Correspondence to László Kérchy.

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Gamal’, M.F., Kérchy, L. Quasiaffine transforms of Hilbert space operators. Acta Sci. Math. (Szeged) 89, 147–165 (2023). https://doi.org/10.1007/s44146-023-00057-y

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  • DOI: https://doi.org/10.1007/s44146-023-00057-y

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