2024/06/11 by María José González, González, María José, Fernando León-Saavedra +1 · 1 citation
Mathematics · #30J05 #47B35 #47B38 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2406.07656
openalex publication_date 2024/06/11 · openalex created_date 2024/06/15 · openalex updated_date 2026/08/03
In this paper we study the minimality of the commutant of an analytic Toeplitz operator Mφ, when Mφ is defined on the Hardy space H2(\mathbbD) and φ∈ H^∞(\mathbbD), denotes a bounded analytic function on \mathbbD. Specifically we show that the commutant of Mφ is minimal if and only if the polynomials on φ are weak-star dense in H^∞(\mathbbD), that is, φ is a weak-star generator of H^∞(\mathbbD). We use our result to characterize when the double commutant of an analytic Toeplitz operator Mφ is minimal, for a large class of symbols φ. Namelly, when φ is an entire function, or more generally when φ belongs to the Thomson-Cowen's class.