Linear maps on the space of all bounded observables preserving maximal deviation

Hilbert isometries and maximal deviation preserving maps on JB-algebras

In this paper we characterize the surjective linear variation norm isometries on JB-algebras. Variation norm isometries are precisely the maps that preserve the maximal deviation, the quantum analogue of the standard deviation, which plays an important role in quantum statistics. Consequently, we characterize the Hilbert's metric isometries on cones in JB-algebras.

可换极大不等式与保持态作用的可算群

Non-Commutative Maximal Inequalities for State-Preserving Actions of amenable groups

本文研究了可算群在非可换$ L^1 $空间上保持态作用的极大不等式及遍历定理，并通过Neveu分解得到随机遍历定理。

状态保持作用下与倍增条件相关的极大不等式

Maximal Inequality Associated to Doubling Condition for State Preserving Actions

本文针对满足倍增条件的顺从局部紧群在冯·诺依曼代数上的状态保持作用，利用Hardy-Littlewood极大不等式、转移原理及遍历平均与鞅的范数估计，证明了极大不等式与遍历定理。