%0 Journal Article 
%A González Fuentes, María José
%A León Saavedra, Fernando
%T Minimal commutant and double commutant property for analytic Toeplitz operators
%D 2025
%@ 2662-2033
%U http://hdl.handle.net/10498/38177
%X 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(D) and φ∈H∞(D) denotes a bounded analytic function in D. Specifically, we show that the commutant of Mφ is minimal if and only if the polynomials on φ are weak star dense in H∞(D), that is, φ is a weak star generator of H∞(D). 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. Specifically, when φ is an entire function, or more generally, when φ belongs to the Thomson–Cowen class.
%K Analytic Toeplitz operator
%K Double commutant property
%K Minimal commutant
%~ Universidad de Cádiz