Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) =...Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.展开更多
In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanis...In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.展开更多
Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an a...Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.展开更多
基金supported by the National Natural Science Foundation of China(No.11526123,No.11401273)the Natural Science Foundation of Shandong Province of China(No.ZR2015PA010)
文摘Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.
基金The first author is supported by Natural Science Foundation of Shandong Province,China(Grant No.ZR2015PA010)National.Natural Science Foundation of China(GrantNo.11526123)The third author is supported by the National Natural Science Foundation of China(Grant No.11401273).
文摘In this paper,we prove that every*-Lie derivable mapping on a von Neu-mann algebra with no central abelian projections can be expressed as the sum of anadditive*-derivation and a mapping with image in the center vanishing at commuta-tors.
基金supported by the National Natural Science Foundation of China(No.11371279)the Shandong Provincial Natural Science Foundation of China(No.ZR2015PA010)
文摘Extending the notion of Haagerup property for finite von Neumann algebras to the general von Neumann algebras, the authors define and study the(**)-Haagerup property for C*-algebras in this paper. They first give an answer to Suzuki's question(2013), and then obtain several results of(**)-Haagerup property parallel to those of Haagerup property for C*-algebras. It is proved that a nuclear unital C*-algebra with a faithful tracial state always has the(**)-Haagerup property. Some heredity results concerning the(**)-Haagerup property are also proved.
