Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence

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Abstract

We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

Original languageEnglish
Pages (from-to)451-463
Number of pages13
JournalActa Scientiarum Mathematicarum
Volume84
Issue number3-4
DOIs
Publication statusPublished - Jan 1 2018

Keywords

  • Geodesic correspondence
  • Operator means
  • Positive definite cone
  • Preservers

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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