Nonlinear *-Jordan-type derivations on *-algebras
Changjing Li, Yuanyuan Zhao, Fangfang Zhao
Abstract
Let π be a unital β-algebra with the unit I. Assume that π contains a nontrivial projection P which satisfies XπP=0 implies X=0 and Xπ(IβP)=0 implies X=0. In this paper, it is shown that Ξ¦ is a nonlinear β-Jordan-type derivation on π if and only if Ξ¦ is an additive β-derivation. As applications, the nonlinear β-Jordan-type derivations on prime β-algebras, von Neumann algebras with no central summands of type I1, factor von Neumann algebras and standard operator algebras are characterized.
Topics & Concepts
MathematicsVon Neumann architectureType (biology)UnitalVon Neumann algebraPure mathematicsProjection (relational algebra)Jordan algebraPrime (order theory)Nonlinear systemOperator algebraAlgebra over a fieldCombinatoricsAlgebra representationPhysicsBiologyAlgorithmQuantum mechanicsEcologyAdvanced Topics in AlgebraAdvanced Operator Algebra ResearchAlgebraic structures and combinatorial models