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

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Jordan Isomorphism
Unitarily Invariant Norm
Geometric mean
Operator Algebras
Bijective
Von Neumann Algebra
Positive definite
Invertible
Algebra
Geodesic
Mathematical operators
Cones
Multiplication
Cone
Correspondence
Restriction
Norm

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence. / Molnár, L.

In: Acta Scientiarum Mathematicarum, Vol. 84, No. 3-4, 01.01.2018, p. 451-463.

Research output: Contribution to journalArticle

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