Superposition operators, -universal functions, and the hyperbolic composition operator

Mortini, Raymond

doi:10.1007/s10474-012-0251-2

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U (H) Has Finite Codimension (And Is Hence Closed)1

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2021

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Cited by 3 publications

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“…The hyperbolic automorphism induced C Φ has been studied extensively during the last thirty years where Φ(z) = z + b bz + 1 with 0 < b < 1 and having fixed points at 1 and −1 (see for instance [6], [9], [11], [12], [13]). Our focus here is on the non-automorphic case where ϕ has a fixed point in S 1 and another one outside D (possibly at ∞).…”

Section: U (H) Has Finite Codimension (And Is Hence Closed)mentioning

confidence: 99%

Universal composition operators

Carmo¹,

Noor²

2021

J. Operator Theory

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A Hilbert space operator U is called \textit{universal} (in the sense of Rota) if every Hilbert space operator is similar to a multiple of U restricted to one of its invariant subspaces. It follows that the \textit{invariant subspace problem} for Hilbert spaces is equivalent to the statement that all minimal invariant subspaces for U are one dimensional. In this article we characterize all linear fractional composition operators Cϕf=f∘ϕ that have universal translates on both the classical Hardy spaces H2(C+) and H2(D) of the half-plane and the unit disk, respectively. The new example here is the composition operator on H2(D) with affine symbol ϕa(z)=az+(1−a) for $0

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