We prove that if there exists an into linear isometry between non-commutative Lp-spaces then there exists an into Jordan * -isomorphism between underlying von Neumann algebras, as an application of Araki-Bunce-Wright's theorem concerning the characterization of orthogonality preserving positive maps between preduals. Moreover, we determine the structure of a linear non-commutative Lp-isometry when it is surjective and *-preserving.
Cite this article
Keiichi Watanabe, An Application of Orthoisomorphisms to Non-Commutative <i>L<sup>p</sup></i>-Isometries. Publ. Res. Inst. Math. Sci. 32 (1996), no. 3, pp. 493–502DOI 10.2977/PRIMS/1195162853