Linear bijections on von Neumann factors commuting with λ-Aluthge transform

Fernanda Botelho, L. Molnár, Gergö Nagy

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We prove that a bijective linear transformation between von Neumann factors that commute with a λ-Aluthge transform is necessarily a non-zero scalar multiple of an algebra ∗-isomorphism in the case of algebras that are not of type I2. As for type I2 factors, that is, in the particular case of the algebra of 2 by 2 complex matrices, we also present a complete description of those transformations which is a bit different. Namely, non-zero scalar multiples of the sum of an algebra ∗-antiisomorphism and the negative of the trace functional times the identity also show up.

Original languageEnglish
Pages (from-to)74-84
Number of pages11
JournalBulletin of the London Mathematical Society
Volume48
Issue number1
DOIs
Publication statusPublished - Feb 25 2015

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Aluthge Transform
Bijection
Algebra
Scalar
Bijective
Linear transformation
Commute
Isomorphism
Trace

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Linear bijections on von Neumann factors commuting with λ-Aluthge transform. / Botelho, Fernanda; Molnár, L.; Nagy, Gergö.

In: Bulletin of the London Mathematical Society, Vol. 48, No. 1, 25.02.2015, p. 74-84.

Research output: Contribution to journalArticle

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