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Rota's universal operators and invariant subspaces in Hilbert spaces

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Cowen, Carl C. and Gallardo Gutiérrez, Eva A. (2016) Rota's universal operators and invariant subspaces in Hilbert spaces. Journal of Functional Analysis, 271 (5). pp. 1130-1149. ISSN 00221236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123616301252


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Abstract

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 particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.


Item Type:Article
Uncontrolled Keywords:Invariant subspaces; Rota's universal operators
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:39918
Deposited On:05 Nov 2016 16:52
Last Modified:07 Nov 2016 15:07

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