Surjective $L^p$-isometries of 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.Proof of Theorem 1.3. We only need to prove the theorem under the further assumption that c ∈ (0, 1/2]. By Lemma 3.5, we may assume that M 1 = M 2 and τ 1 = τ 2 . Recall that φ preserves the orthogonality in both direction. Then the theorem is an immediate consequence of Theorem 1.2 in [5], Theorem 4.9 in [8] and Theorem 3.1.