# Journal of Operator Theory

Volume 87, Issue 2, Spring 2022 pp. 389-412.

$L^p$-isometries of Grassmann spaces in\\ factors of type $\mathrm{II}$

**Authors**:
Weijuan Shi (1), Junhao Shen (2), Weichen Gu (3), Minghui Ma (4)

**Author institution:** (1) School of Mathematics and Statistics, Shaanxi Normal University,
Xi'an, 710062, China

(2) Department of Mathematics and Statistics, University of
New Hampshire, Durham, 03824, U.S.A.

(3) School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

(4) School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

**Summary: **Let $ \mathcal M $ be a factor of type $\mathrm{II}$ with a faithful normal semifinite tracial weight $\tau$, and $\mathscr P$ the set of all projections in $\mathcal M$.
Denote by $\mathscr P_{c}$ the Grassmann space of all projections in $\mathscr P$ with trace $c$, where $c$ is a positive real number.
The aim of this paper is to describe the general form of $L^p$-isometries between Grassmann spaces in a factor of type II. Moreover, we prove that, when $0

**DOI: **http://dx.doi.org/10.7900/jot.2020sep30.2352

**Keywords: **orthoisomorphism, Grassmann spaces, projections

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