Bounded Toeplitz operators and unbounded projected multiplication
Abstract
We construct a smooth, nonnegative radial symbol $g$ on $\mathbb C$ whose Toeplitz operator on Bargmann--Fock space is positive with singular values decaying faster than every exponential, while projected multiplication $f\mapsto P(gf)$ has no bounded extension from the ambient Gaussian $L^2$ space. All heat transforms of $g$ at positive times are Schwartz functions, and $g\in L^p(dA)$ for every $0
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint