发表机构
Institute for Advanced Study in Mathematics of HIT, Harbin Institute of Technology; Harbin Institute of Technology（哈尔滨工业大学数学高等研究院; 哈尔滨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了Marcinkiewicz空间单位球的极值点，证明非交换情形下正等距为初等形式，并研究了弱$L_p$空间等上的等距及其单参数群。
AI 中文摘要
我们刻画了Marcinkiewicz空间在其自然拟范数下（正）单位球的极值点。基于这些结果，我们证明非交换Marcinkiewicz空间上的每个正等距都具有初等形式。特别地，在原子von Neumann代数上（所有原子具有相同迹）的非交换Marcinkiewicz空间上的线性映射是正满射等距当且仅当它是保持奇异值函数的Jordan $*$-同构的限制。我们还研究了与$\sigma$-有限非原子von Neumann代数关联的弱$L_p$空间（$1<p<\infty$）、Marcinkiewicz序列空间以及弱$\ell_p$算子理想（$p>0$）上的（不一定正的）满射等距，以及后两者上的单参数等距群。
英文摘要
We characterize extreme points of the (positive) unit ball of Marcinkiewicz spaces with respect to their natural quasi-norms. Having these results at hand, we show that every positive isometry on a noncommutative Marcinkiewicz space is of elementary form. In particular, a linear mapping on a noncommutative Marcinkiewicz space over an atomic von Neumann algebra with all atoms having the same trace is a positive surjective isometry if and only if it is the restriction of a Jordan $*$-isomorphism which preserves the singular value functions. We also study (not necessarily positive) surjective isometries on weak $L_p$-spaces affiliated a $σ$-finite non-atomic von Neumann algebra for $1<p<\infty$, Marcinkiewicz sequence spaces, and weak $\ell_p$ operator ideals, $p>0$, as well as one-parameter groups of isometries on the latter two.
