Author

Zijian Zeng

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Preprint Aug 2026

Fixed Convex-Lens Spectral Constants: M\"obius Reduction, Sharp Model Theorems, and Angle-Dependent Bounds

For the intersection of two disks meeting at angle $2\alpha$, let $C(\alpha)$ be the least constant in the associated spectral-set inequality. We give a self-contained M"obius reduction to the corresponding numerical-range problem on a sector and determine the sharp constant for affine square-zero operators $B=\lambda...

Zi-Jian Zeng · 0 citations

Preprint Aug 2026

A Counterexample to the Tang Zhang Schatten Norm Conjecture and Sharp Positive Results

For $m\geq 2$, let $c_p(m)$ be the all-dimensional best constant in $$ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p. $$ Tang and Zhang conjectured an explicit formula for every finite $p>1$. We disprove the conjecture with two explicit real $2\times 2$ rank-one matrices at $p=3/2$. T...

Zi-Jian Zeng, Hou-De Liu, Kurunathan Ratnavelu · 2 citations