Essential norm and integration of a family of weighted composition operators

2025/05/27 by David Norrbo, Norrbo, David
Computer Science · Mathematics · #30H20 (Secondary) #47B91 (Primary) 47G10 #Approximation Theory and Sequence Spaces #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2505.21268

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the interchange of essential norm and integration of certain families of weighted composition operators acting on the standard weighted Bergman spaces A^p_α, where p>1 and α≥ 0. To be more precise, we give a sufficient condition for ‖∫ u_tC_ϕt dt‖_e = ∫ ‖ u_tC_ϕt‖_e dt to hold in terms of geometric properties of u_t and ϕ_t. We also provide some necessary conditions for the equality to hold and calculate the essential norm of some integral operators such as some Volterra operators.

Citations

• Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces
• Property (M), M-ideals, and almost isometric structure of Banach\n spaces

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