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Browsing by Subject "universal operators"
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Item A hyperbolic universal operator commuting with a compact operator(AMS, 2019) Cowen, Carl C.; Gallardo-Gutiérrez, Eva A.; Mathematical Sciences, School of ScienceA 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 non-trivial, quasinilpotent, injective, compact operator with dense range, but unlike other examples, it acts on the Bergman space instead of the Hardy space and this operator is associated with a `hyperbolic' composition operator.Item A new proof of a Nordgren, Rosenthal and Wintrobe Theorem on universal operators(American Mathematical Society, 2017) Cowen, Carl C.; Gallardo-Gutiérrez, Eva A.A striking result by Nordgren, Rosenthal and Wintrobe states that the Invariant Subspace Problem is equivalent to the fact that any minimal invariant subspace for a composition operator Cφ induced by a hyperbolic automorphism φ of the unit disc D acting on the classical Hardy space H² is one dimensional. We provide a completely different proof of Nordgren, Rosenthal and Wintrobe’s Theorem based on analytic Toeplitz operators.