Strict singularity of weighted composition operators on derivative Hardy spaces

2019/03/25 by Qingze Lin, Lin, Qingze, Jun‐Ming Liu +3
Mathematics · #30H05 #47B33 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1903.10265

openalex publication_date 2019/03/25 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

We prove that the weighted composition operator W_ϕ,φ fixes an isomorphic copy of ℓ^p if the operator W_ϕ,φ is not compact on the derivative Hardy space S^p. In particular, this implies that the strict singularity of the operator W_ϕ,φ coincides with the compactness of it on S^p. Moreover, when p≠2, we characterize the conditions for those weighted composition operators W_ϕ,φ on S^p which fix an isomorphic copy of ℓ² .

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