Generalized Cesàro operators in weighted Banach spaces of analytic functions with sup-norms

2024/02/06 by Angela A. Albanese, Albanese, Angela A., José Bonet +3 · 2 citations
Mathematics · #47A10 #47A16 #47A35 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 46E15 #Secondary 46E10

paper · pdf · doi:10.48550/arxiv.2402.04003

openalex publication_date 2024/02/06 · openalex created_date 2024/02/08 · openalex updated_date 2026/07/28

Abstract

An investigation is made of the generalized Cesàro operators C_t, for t∈ [0,1], when they act on the space H(\mathbbD) of holomorphic functions on the open unit disc \mathbbD, on the Banach space H^∞ of bounded analytic functions and on the weighted Banach spaces H_v^∞ and H_v⁰ with their sup-norms. Of particular interest are the continuity, compactness, spectrum and point spectrum of C_t as well as their linear dynamics and mean ergodicity.

Cited by

• Optimal domain of Volterra operators in classes of Banach spaces of analytic functions
• The Rhaly Operators on Köthe Spaces

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