Optimal 2-uniform convexity of Schatten classes revisited

对Schatten类等距嵌入性的重新审视

Isometric Embeddability of Schatten Classes Revisited

本文总结了Schatten类间等距嵌入存在的已知结果与开放问题，并通过新方法获得非嵌入性结果，概述了相关方法。

Convexity of quasi-entropy type functions: Lieb's and Ando's convexity theorems revisited

Given a positive function $f$ on $(0,\infty)$ and a non-zero real parameter $θ$, we consider a function $I_f^θ(A,B,X)=Tr X^*(f(L_AR_B^{-1})R_B)^θ(X)$ in three matrices $A,B>0$ and $X$. In the literature $θ=\pm1$ has been typical. The concept unifies various quantum information quantities such as quasi-entropy, monotone metrics, etc. We characterize joint convexity/concavity and monotonicity properties of the function $I_f^θ$, thus unifying some known results for various quantum quantities.

Impressions of convexity - An illustration for commutator bounds

We determine the sharpest constant $C_{p,q,r}$ such that for all complex matrices $X$ and $Y$, and for Schatten $p$-, $q$- and $r$-norms the inequality $$ \|XY-YX\|_p\leq C_{p,q,r}\|X\|_q\|Y\|_r $$ is valid. The main theoretical tool in our investigations is complex interpolation theory.

Clarkson-McCarthy inequalities with unitary and isometry orbits

A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten $p$-classes for p>2 is proved

Banach空间子空间和凸锥的度量几何再探

The metric geometry of subspaces and convex cones of the Banach space revisited

本文证明了在一致凸和一致光滑的Banach空间中，子空间的度量投影线性与凸锥极集的凸性等价，并等价于空间为内积空间。

Arazy关于Schur乘子的猜想：重访与解决

Arazy's conjecture concerning Schur multipliers: revisited and resolved

本文解决了Arazy关于Schur乘子有界性的猜想，确定了Schur-Hadamard乘子从$\mathcal{S}^q$到$\mathcal{S}^p$有界的精确条件，并给出了新证明。