collaborators
Showing math.FAShow all

5 papers · 1 filter

math.FA2026

Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons

Sam Looi

Let be a positive Borel measure on $\C^n$. For every , we prove that the Toeplitz operator induced by on pluriharmonic Fock space belongs to…

math.FA2026

When the Berezin transform fails to detect compactness: Toeplitz operators with symbols on weighted Bergman spaces

Sam Looi

For every and , we construct whose Toeplitz form extends to a bounded, noncompact operator on the weighted Bergman spaces $A^2_γ(\mathbb…

math.FA2026

Positive Berezin liminf does not imply essential positivity for radial Toeplitz operators on Bergman and Fock spaces

Sam Looi

We study whether essential positivity \[ σ_{\mathrm{ess}}(T_f)\subset [0,\infty) \] of a radial Toeplitz operator on Bergman and Fock spaces can be detected from the asymptotic be…

math.FA2026

A counterexample to the Berger--Coburn conjecture

Sam Looi

Berger and Coburn proposed an endpoint boundedness criterion for Toeplitz operators on the Bargmann--Fock space in which the decisive quantity is the heat transform of the symbol a…

math.FA2026

Unbounded symbols, heat flow, and Toeplitz operators

Sam Looi

We disprove the natural domain extension of the Berger--Coburn heat-flow conjecture for Toeplitz operators on the Bargmann space and identify the failure mechanism as a gap between…