Publications of the Research Institute for Mathematical Sciences
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An Application of Orthoisomorphisms to Non-Commutative Lp-IsometriesKeiichi Watanabe (1) Department of Mathematics, Niigata University, 8050 Ikarashi 2-no-cho, Nishi-ku, 950-2181, NIIGATA, JAPAN
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.
Watanabe Keiichi: An Application of Orthoisomorphisms to Non-Commutative Lp-Isometries. Publ. Res. Inst. Math. Sci. 32 (1996), 493-502. doi: 10.2977/prims/1195162853