Nonlinear Lie-type derivations of von Neumann algebras and related topics

• Autorzy: Ajda Fošner , Feng Wei , Zhankui Xiao
• Języki publikacji: EN

Abstrakty

EN

Motivated by the powerful and elegant works of Miers (1971, 1973, 1978) we mainly study nonlinear Lie-type derivations of von Neumann algebras. Let 𝓐 be a von Neumann algebra without abelian central summands of type I₁. It is shown that every nonlinear Lie n-derivation of 𝓐 has the standard form, that is, can be expressed as a sum of an additive derivation and a central-valued mapping which annihilates each (n-1)th commutator of 𝓐. Several potential research topics related to our work are also presented.

Kategorie tematyczne

• 46L57: Derivations, dissipations and positive semigroups in C * -algebras
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 132
• Numer: 1
• Strony: 53-71

Daty

wydano

2013

Twórcy

autor

Ajda Fošner

• Faculty of Management, University of Primorska, Cankarjeva 5, SI-6104 Koper, Slovenia

autor

Feng Wei

• School of Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China

autor

Zhankui Xiao

• School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, 362021, P.R. China

Identyfikatory

DOI

10.4064/cm132-1-5