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Abstract: In this paper, we prove that every bijective map preserving Lie products from a factor von Neumann algebra into another factor von Neumann algebra is of the form , where is an additive isomorphism or the negative of an additive anti-isomorphism and is a map with for all . [Copyright &y& Elsevier]

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

Abstract: Let be a nest on a complex separable Hilbert space H, and be the associated nest algebra. In this paper, we prove that every biderivation of is an inner biderivation if and only if dim0+ ≠1 or , and that every generalized biderivation of is an inner generalized biderivation if dim0+ ≠1 and . [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]

Abstract: In this paper, it is proved that every surjective linear map preserving identity and zero products in both directions between two nest subalgebras with non-trivial nests of any factor von Neumann algebra is an isomorphism; and that every surjective weakly continuous linear map preserving identity and zero Jordan products in both directions between two nest subalgebras with non-trivial nests of any factor von Neumann algebra is either an isomorphism or an anti-isomorphism. [Copyright &y& Elsevier]

Abstract: In this paper, it is proved that every surjective weakly continuous linear local automorphism of nest subalgebras with non-trivial nests of factor von Neumann algebras is an automorphism; and that every surjective linear 2-local automorphism of nest algebras with non-trivial nests of factor von Neumann algebras is an automorphism. [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]