2019/11/15 by João R. Carmo, Carmo, João R., S. Waleed Noor +1 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1911.06763
openalex publication_date 2019/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A Hilbert space operator U is called 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 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 Cϕ f=f∘ϕ that have universal translates on both the classical Hardy spaces H2(ℂ+) and H2(\mathbbD) of the half-plane and the unit disk respectively. The surprising new example is the composition operator on H2(\mathbbD) with affine symbol ϕa(z)=az+(1-a) for 0