Structural rigidity of generalised Volterra operators on H^p

2017/10/03 by Santeri Miihkinen, Pekka Nieminen, Miihkinen, Santeri +5
Mathematics · #47B10 #47G10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1710.01252

openalex publication_date 2017/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the non-compact generalised analytic Volterra operators T_g, where g ∈ BMOA, have the following structural rigidity property on the Hardy spaces H^p for 1 ≤ p < ∞ and p ≠ 2: if T_g is bounded below on an infinite-dimensional subspace M ⊂ H^p, then M contains a subspace linearly isomorphic to ℓ^p. This implies in particular that any Volterra operator T_g\colon H^p → H^p is ℓ²-singular for p ≠ 2.

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