Equivalent characterization of ∗-derivations on von Neumann algebras. Issue 3 (4th March 2019)

• Record Type: Journal Article
• Authors: Fu, Feiyan; An, Runling
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 3(2019)
• Page Start: 527
• Page End: 541
• Publication Date: 2019-03-04
• Subjects: von Neumann algebras -- skew Lie product -- ∗-derivations; 16W25 -- 46L57 -- 47B47; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1425355
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: LetM be a von Neumann algebra with no central abelian projections. In this paper, it is shown thatΦ : M → M is a non-linear skew Lie-triple derivation (that is, Φ ( [ [ A, B ] ∗, C ] ∗ ) = [ [ Φ ( A ), B ] ∗, C ] ∗ + [ [ A, Φ ( B ) ] ∗, C ] ∗ + [ [ A, B ] ∗, Φ ( C ) ] ∗, ∀ A, B, C ∈ M ) if and only if it is a ∗ -derivation, where[ A, B ] ∗ = A B - B A ∗ . In particular, ifM is a factor von Neumann algebra, thenΦ : M → M is a non-linear skew Lie-triple derivation if and only if there existsT ∈ M withT ∗ = - T such thatΦ ( A ) = A T - T A for allA ∈ M .