T. Vuong

collaborators

8 papers

math.FA2026

Positive Planar Measures for Spectral Pinching and the Corrected BMV Conjecture

Trung Hoa Dinh, Cong Trinh Le, Trung Dung Vuong

We prove the corrected Bessis--Moussa--Villani pinching conjecture for all symmetrized word averages. For Hermitian matrices $A, B$ and $D = E_{A} (B)$ , we construct a positive compactly…

math.OA2026

Three-Point Trace Positivity:Schatten Norm Compression and Interpolating Metrics

Trung Dung Vuong, Hiroyuki Osaka

Let $(N, ν)$ be a finite tracial von Neumann algebra and set $K_{r} (P, Q) = ν ((P^{1/2} Q P^{1/2})^{r})$ . We prove that $$ [\mathcal{K}_r(P_i,P_j)]_{i,j=1}^3\ge0, \qquad 1/…

math.FA2026

Weighted Two-Parameter Quantum Divergences Generated by Matrix Power-Mean Gaps

Trung Hoa Dinh, Minh Toan Ho, Ha Trang Nguyen +1

Let $P_{n}$ be the cone of $n \times n$ complex positive definite matrices. For $0 < θ < 1$ and $r \geq 0$ , let $M_{r}^{(θ)}$ denote the weighted matrix power mean, with the logarithm…

math.AG2026

Determinantal Kernel Schemes of Matrix Nets and Applications to Positive Maps

Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le +1

For a linear map on a matrix space, we study the projective schemes obtained by intersecting its projectivized kernel with determinantal rank loci. For matrix nets, that is, three…

math-ph2026

Alternative-mean trace divergences: geometry, data processing, and barycenters

Trung Dung Vuong, Hiroki Shudo, Hiroyuki Osaka

Let $f : (0, \infty) \to (0, \infty)$ be a nontrivial normalized operator monotone function and set $s = f^{'} (1)$ . We introduce the alternative-mean trace functional $$ \altPhi_f(A,B) :=\Tr(…

math.FA2026

Sharp Hyperbolic Cutoffs and Dimension-Sharp Counterexamples for Reverse Araki-Type Inequalities

Trung Dung Vuong

We study reverse Araki-type trace inequalities and log-majorizations beyond the exponent $2$ . For arbitrary nonnegative nondecreasing weights, we show that $s = 2$ is the sharp dimen…

quant-ph2026

Polar Fidelities, Holevo Bases, and Unitary Factors of Generalized Fidelity

Trung Dung Vuong

Motivated by several open problems in the Afham-Ferrie theory of generalized fidelity, we study polar fidelities, Holevo bases, and unitary factors on $\Pd$, the cone of \(d\time…

math.FA2026

Heron-Wasserstein majorization inequalities for spectral and Kubo-Ando geometric means

Trung Dung Vuong, Anh Thi Nguyen, Trung Hoa Dinh

We prove sharp Heron-type majorization inequalities for two quadratic matrix expressions associated with the spectral and Kubo-Ando geometric means. For the spectral geometric mean…