Journal of Operator Theory

Volume 89, Issue 1, Winter 2023 pp. 183-204.

Invariant subspaces of weighted Bergman spaces in infinitely many variables

Authors: Hui Dan (1), Kunyu Guo (2), Jiaqi Ni (3)
Author institution: (1) College of Mathematics, Sichuan University, Chengdu, 61006-5, China
(2) School of Mathematical Sciences, Fudan University, Shanghai, 200433, China and Scool of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, China
(3) School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

Summary: This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space $A_{\beta}^2$ in infinitely many variables. We completely classify these invariant subspaces under the unitary equivalence. Our results not only cover cases of both the Hardy space $H^{2}(\mathbb{D}_{2}^{\infty})$ and the Bergman space $A^{2}(\mathbb{D}_{2}^{\infty})$ in infinitely many variables, but also apply in finite variable setting.

DOI: http://dx.doi.org/10.7900/jot.2021may18.2330
Keywords: invariant subspace, unitary equivalence, Hilbert module, Hardy space, weighted Bergman space, infinitely many variables

Contents Full-Text PDF