Zhekai Pang

collaborators

5 papers

math.FA2026

Counterexamples to a conjectured Schatten norm inequality

Zhekai Pang

For $p \geq 1$ and $m \geq 2$ , let $c_{p} (m)$ be the least constant such that \[ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p \] for all square comp…

math.RA2026

Counterexamples to a multivariable matrix Young conjecture

Zhekai Pang

We disprove Conjecture 5.1 of Lin concerning a multivariable extension of Ando's matrix Young inequality for positive semidefinite matrices. For every integer $m \geq 4$ , the conject…

math.RA2026

Proof of Dittert's conjecture for dimensions \texorpdfstring{$n\ge 17$}{n >= 17}

Zhekai Pang

Dittert's conjecture gives a sharp upper bound for the Dittert functional on nonnegative matrices whose entries sum to $n$. It extends the van der Waerden permanent problem from…

math.RA2026

Real Matrices as Linear Combinations of Three Orthogonal Matrices

Zhekai Pang

Li and Poon proved that every real square matrix is a real linear combination of four real orthogonal matrices. The resulting question, recorded by Zhan, asks whether four terms ar…

math.PR2026

Absolute moment inequalities under quadratic-form positivity

Zhekai Pang

We prove the open question posed by Zhuang and Hu in Remark 3.1. More generally, we consider symmetric joint probability mass functions and joint densities whose associated quadrat…

Counterexamples to a conjectured Schatten norm inequality

Counterexamples to a multivariable matrix Young conjecture

Proof of Dittert's conjecture for dimensions \texorpdfstring{\(n\ge 17\)}{n >= 17}

Real Matrices as Linear Combinations of Three Orthogonal Matrices

Absolute moment inequalities under quadratic-form positivity