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Bounded symbols and one-component geometry
Sam Looi
We prove that every bounded truncated Toeplitz operator on a Hardy model space admits a bounded symbol if and only if its defining inner function is one-component, meaning that it…
Stability of isometries of quantum states
Sam Looi
We prove dimension-independent Hyers--Ulam stability for surjective approximate isometries of the positive trace-class cone in both the trace and Bures metrics. Here $\varepsilon\g…
Comparing positive Toeplitz operators on holomorphic and pluriharmonic Fock spaces
Sam Looi
We prove sharp norm comparisons between positive Toeplitz operators associated with the same positive Borel measure, acting respectively on holomorphic functions and on sums of hol…
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…
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 beh…
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…
Bounded Toeplitz operators and unbounded projected multiplication
Sam Looi
We construct a smooth, nonnegative radial symbol on whose Toeplitz operator on Bargmann--Fock space is positive with singular values decaying faster than every expo…