Surjective $L^p$-isometries of Grassmann spaces

TL;DR

This paper characterizes all surjective $L^p$-isometries between Grassmann spaces of projections with equal trace in semifinite factors, extending previous work on unitary groups.

Contribution

It provides a complete description of surjective $L^p$-isometries of Grassmann spaces in semifinite factors, generalizing known results from finite factors.

Findings

Characterization of all surjective $L^p$-isometries in the setting of semifinite factors.

Extension of previous finite factor results to semifinite factors.

New insights into the structure of isometries in Grassmann spaces.

Abstract

Based on the characterization of surjective $L^p$-isometries of unitary groups in finite factors, we describe all surjective $L^p$-isometries between Grassmann spaces of projections with the same trace value in semifinite factors.