JournalsprimsVol. 32 , No. 3DOI 10.2977/prims/1195162853

An Application of Orthoisomorphisms to Non-Commutative <i>L<sup>p</sup></i>-Isometries

  • Keiichi Watanabe

    Niigata University, Japan
An Application of Orthoisomorphisms to Non-Commutative <i>L<sup>p</sup></i>-Isometries cover

Abstract

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.