### 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 I_{2}. As for type I_{2} 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 language | English |
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Pages (from-to) | 74-84 |

Number of pages | 11 |

Journal | Bulletin of the London Mathematical Society |

Volume | 48 |

Issue number | 1 |

DOIs | |

Publication status | Published - Feb 25 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Bulletin of the London Mathematical Society*,

*48*(1), 74-84. https://doi.org/10.1112/blms/bdv092

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

Research output: Contribution to journal › Article

*Bulletin of the London Mathematical Society*, vol. 48, no. 1, pp. 74-84. https://doi.org/10.1112/blms/bdv092

}

TY - JOUR

T1 - Linear bijections on von Neumann factors commuting with λ-Aluthge transform

AU - Botelho, Fernanda

AU - Molnár, L.

AU - Nagy, Gergö

PY - 2015/2/25

Y1 - 2015/2/25

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84962259288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84962259288&partnerID=8YFLogxK

U2 - 10.1112/blms/bdv092

DO - 10.1112/blms/bdv092

M3 - Article

VL - 48

SP - 74

EP - 84

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 1

ER -