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oai:docta.ucm.es:20.500.14352/246092024-07-12T14:54:44Zcom_20.500.14352_14col_20.500.14352_15

Rota’s universal operators and invariant subspaces in Hilbert spaces Cowen, Carl C. Gallardo Gutiérrez, Eva Antonia A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In articular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator. 2023-06-18T06:55:51Z 2023-06-18T06:55:51Z 2023-06-18T06:55:51Z 2016 journal article https://hdl.handle.net/20.500.14352/24609 0022-1236 10.1016/j.jfa.2016.05.018 eng MTM2010-16679 MTM2013-42105-P Cowen, C. C., & Gallardo Gutiérrez, E. A. «Rota’s Universal Operators and Invariant Subspaces in Hilbert Spaces». Journal of Functional Analysis, vol. 271, n.o 5, septiembre de 2016, pp. 1130-49. DOI.org (Crossref), https://doi.org/10.1016/j.jfa.2016.05.018. restricted access Elsevier