Extreme points of the unit balls and isometries of noncommutative quasi-Banach Marcinkiewicz spaces
Year: 2026
Type: preprint
Abstract: We characterize extreme points of the (positive) unit balls of Marcinkiewicz spaces with respect to their natural quasi-norms. Having these results at hand, we show that every positive surjective 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 $10$, as well as one-parameter groups of isometries on the latter two.
Source: arXiv (Cornell University)
Authors: Fang, Kai, Gao, Yi, Huang, Jinghao, Sukochev, Fedor
Institutions: Harbin Institute of Technology, UNSW Sydney
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7219155338