2025/03/18 by Bouhali, Aissa, Louhichi, Issam, Yousef, Abdel Rahman
#Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 47B35 #Secondary 47L80
paper · doi:10.48550/arxiv.2503.14200
A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute with it. In this paper, we provide a complete description of bounded Toeplitz operators Tf, where the symbol f has a truncated polar decomposition, that commute with a Toeplitz operator whose symbol is the sum of a quasihomogeneous function and a bounded analytic function.