Search

Abstract: In this note, it is shown that every Jordan derivation of triangular algebras is a derivation. [Copyright &y& Elsevier]

Abstract: In this paper, it is proved that every weakly continuous local 2-cocycle of a nest subalgebra of a factor von Neumann algebra with coefficients in the factor von Neumann algebra is a 2-cocycle. [Copyright &y& Elsevier]

Abstract: Let be a nest on a complex separable Hilbert space , and be the associated nest algebra. In this paper, we prove that every Lie triple derivation from into itself is of the form X → XT − TX + h(X)I, where and h is a linear mapping from into such that h([[A, B], C])=0 for all . [Copyright &y& Elsevier]

Abstract: In this paper, it is shown that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is generated by finitely many independent nests into any ultraweakly closed subalgebra which contains the algebra is an inner derivation, and that every norm continuous linear local derivation from an arbitrary CSL algebra whose lattice is completely distributive into any ultraweakly closed subalgebra which contains the algebra is a derivation. [Copyright &y& Elsevier]

In this paper, it is proved that every norm continuous linear local derivation of a nest subalgebra of a factor von Neumann algebra is a derivation, and that every linear 2-local derivation of a nest subalgebra of a factor von Neumann algebra is a derivation. [Copyright &y& Elsevier]

In this note, for a C*-algebra A, we define a matrix-trace on the C*-algebra Mn(A) to be a positive linear mapping τ:Mn(A)→A such that τ(u*au)=τ(a) (∀a∈Mn(A), ∀u∈U(Mn(A))) and τ(a2)⩽(τ(a))2 (∀a⩾0). We give some basic properties of a matrix-trace and prove that if A is a unital Abelian C*-algebra, then a map τ is an A-module matrix-trace on Mn(A) if and only if there exists an element λ of A with 0⩽λ⩽λ2 such that τ(a)=λ·tr(a) (∀a=[aij]∈Mn(A)), where tr(a)=∑i=1naii. [Copyright &y& Elsevier]