Isometries on positive definite operators with unit Fuglede-Kadison determinant. (English) Zbl 1442.46044

Summary: In this paper we explore the structure of certain surjective generalized isometries (which are transformations that leave any given member of a large class of generalized distance measures invariant) of the set of positive invertible elements in a finite von Neumann factor with unit Fuglede-Kadison determinant. We conclude that any such map originates from either an algebra \(^*\)-isomorphism or an algebra \(^*\)-antiisomorphism of the underlying operator algebra.


46L10 General theory of von Neumann algebras
46L36 Classification of factors
46L40 Automorphisms of selfadjoint operator algebras
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