A Banach algebra structure on the $q$-Bergman space and related topics
Volume 174 / 2023
Colloquium Mathematicum 174 (2023), 285-300
MSC: Primary 47B47; Secondary 47A15, 47B38
DOI: 10.4064/cm9168-12-2023
Published online: 19 December 2023
Abstract
We show that the $q$-Bergman space with the Duhamel product has a Banach algebra structure and describe its nontrivial closed ideals. Moreover, we discuss Katznelson–Tzafriri type theorems in the $q$-Bergman space. We also give applications to the Volterra integral operator on this space and to some integral equations.
