AI 中文总结
该研究证明李型Schatten范数不等式的sharp线性结果，可无损失传递至任意非负凹函数类，明确了非线性问题与对应线性问题的最优常数一致。
AI 中文摘要
我们针对有限复矩阵族的李型Schatten范数不等式，比较其sharp常数与对相关绝对值应用任意非负凹函数后得到的对应常数。我们证明，对于任意有限矩阵维数、任意求和项数、任意Schatten指数（包括算子范数端点），该非线性问题的最优常数与 underlying 线性问题的完全相同。对于有限指数，证明过程通过无损单cap归约、有限cap组合下的正混合精确表示，以及基于加权Schatten收缩和Araki-Lieb-Thirring不等式的非对易重组论证完成；有限谱cap插值与零点处的扰动论证进而得到一般凹情形。因此，所有sharp线性结果可无损失地传递至全部非负凹函数类。
英文摘要
We compare the sharp constants in Lee-type Schatten norm inequalities for finite families of complex matrices with the corresponding constants obtained after applying an arbitrary nonnegative concave function to the relevant absolute values. We prove that the nonlinear problem has exactly the same best constant as the underlying linear problem for every finite matrix dimension, every number of summands, and every Schatten exponent, including the operator-norm endpoint. For finite exponents, the proof proceeds through a lossless single-cap reduction, an exact representation as a positive mixture for finite cap combinations, and a noncommutative reassembly argument based on a weighted Schatten contraction and the Araki-Lieb-Thirring inequality. Finite-spectrum cap interpolation and a perturbation argument at zero then yield the general concave case. Thus every sharp linear result transfers without loss to the full class of nonnegative concave functions.
Comments11 pages, no figures
