An Application of Orthoisomorphisms to Non-Commutative -Isometries
Keiichi Watanabe
Niigata University, Japan
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Abstract
We prove that if there exists an into linear isometry between non-commutative -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 -isometry when it is surjective and -preserving.
Cite this article
Keiichi Watanabe, An Application of Orthoisomorphisms to Non-Commutative -Isometries. Publ. Res. Inst. Math. Sci. 32 (1996), no. 3, pp. 493–502
DOI 10.2977/PRIMS/1195162853