Anton Baranov, Andrei Lishanskii
Abstract
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Recently, Sophie Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. We give a similar construction using a functional model for rank one perturbations of singular unitary operators.
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Recently, Sophie Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. We give a similar construction using a functional model for rank one perturbations of singular unitary operators.
Key concepts: Unitary state, Unitary operator, Hilbert space, Mathematics, Rank (graph theory), Operator (biology), Perturbation (astronomy), Pure mathematics