## 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.

### MSC:

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

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