Analytic Schur multipliers
Abstract
We study in this paper analytic Schur multipliers on C + 2 \mathbb {C}_{+}^{2} and D 2 \mathbb {D}^{2} , i.e. Schur multipliers on R 2 \mathbb {R}^{2} and T 2 \mathbb {T}^{2} that are boundary-value functions of functions analytic in C + 2 \mathbb {C}_{+}^{2} and D 2 \mathbb {D}^{2} . Such Schur multipliers are important when studying properties of functions of maximal dissipative operators and contractions under perturbation. We show that if the boundary-value function of a Schur multiplier has certain regularity properties, then it can be represented as an element of the Haagerup tensor product of spaces of analytic functions with similar regularity properties.
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Operator Algebra Research
Advanced Banach Space Theory
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 1207–1216
- Publication date
- 14 January 2026
- Language
- EN