Clarkson-McCarthy inequalities with unitary and isometry orbits

从 Clarkson-McCarthy 不等式到 Ball-Carlen-Lieb 不等式

From Clarkson-McCarthy inequality to Ball-Carlen-Lieb inequality

本文利用酉轨道技术、Hadamard 三线定理与对偶论证，推广 Clarkson-McCarthy 不等式并完善 Ball-Carlen-Lieb 的最优2-一致凸性不等式。

若干算子的 Clarkson-McCarthy 不等式的加强

Strengthening of Clarkson-McCarthy inequalities with several operators

本文通过扩展 Bourin-Lee 方法，建立并推广了涉及若干算子的加强型 Clarkson-McCarthy 不等式，证实既有猜想并改进相关结果。

Clarkson-McCarthy型不等式，第一部分：$\ell_p$--$\ell_p$和$\ell_q$--$\ell_p$ Schatten $p$-估计

Clarkson--McCarthy type inequalities, part I: $\ell_p$--$\ell_p$ and $\ell_q$--$\ell_p$ Schatten $p$-estimates

本文基于矩阵U的特性，推导出Clarkson-McCarthy型不等式，涵盖ℓ_p--ℓ_p和ℓ_q--ℓ_p Schatten p-估计，并扩展了Ball-Carlen-Lieb不等式及Audenaert猜想的弱界。

Continuous generalization of Clarkson-McCarthy inequalities

Let $G$ be a compact abelian group, let $μ$ be the corresponding Haar measure, and let $\hat G$ be the Pontryagin dual of $G$. Further, let $C_p$ denote the Schatten class of operators on some separable infinite dimensional Hilbert space, and let $L^p(G;C_p)$ denote the corresponding Bochner space. If $G\niθ\mapsto A_θ$ is the mapping belonging to $L^p(G;C_p)$ then, $$\sum_{k\in\hat G}\left\|\int_G\overline{k(θ)}A_θ\,\mathrm{d}θ\right\|_p^p\le\int_G\|A_θ\|_p^p\,\mathrm{d}θ,\qquad p\ge2$$ $$\sum_{k\in\hat G}\left\|\int_G\overline{k(θ)}A_θ\,\mathrm{d}θ\right\|_p^p\le\left(\int_G\|A_θ\|_p^q\,\mat…

局部紧群上的Clarkson-McCarthy不等式

Clarkson-McCarthy inequality on a locally compact group

本文在局部紧群上证明了一个关于Schatten理想的积分不等式，推广了Clarkson-McCarthy不等式和Hausdorff-Young不等式，并给出推论。