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 language | English |
|---|---|
| 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)
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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 journal › Article
}
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 -