Jordan derivations of full matrix algebras

Let A be a unital associative ring and M be a 2-torsion free A-bimodule. Using an elementary and constructive method we show that every Jordan derivation from M_n(A) into M_n(M) is a derivation.     

On Lie ideals with generalized derivations

Let R be a prime ring with characteristic different from 2, let U be a nonzero Lie ideal of R, and let f be a generalized derivation associated with d. We prove the following results: (i) If a ∈ R and [a, f(U)] = 0 then a ∈ Z or d(a) = 0 or U ? Z; (ii) If f ²(U) = 0 then U ? Z; (iii) If u ² ∈ U for all u ∈ U and f acts as a homomorphism or antihomomorphism on U then either d = 0 or U ? Z.     

AF C~*-代数中的子代数上的保幂等映射和局部导子

证明了从AFC-代数E中的子代数A到任意赋范代数B上的范数连续保幂等映射是Jordan同态,以及从A到任意赋范E-双模M上的局部导子是导子,从而推广了Crist关于局部导子的结果．     

Push-outs of derivations

Let be a Banach algebra and let X be a Banach -bimodule. In studying (,X) it is often useful to extend a given derivation D: → X to a Banach algebra containing as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approximate identities to obtain the extension as a limit of operators b ↦ D(ba) − b.D(a), a ε in an appropriate operator topology, the main point in the proof being to show that the limit map is in fact a derivation. In this paper we make clear which part of this approach is analytic and which algebraic by presenting an algebraic scheme that gives derivations in all situations at the cost of enlarging the module. We use our construction to give improvements and shorter proofs of some results from the literature and to give a necessary and sufficient condition that biprojectivity and biflatness is inherited to ideals.     

Local automorphisms of standard operator algebras

Let X be an infinite-dimensional separable real or complex Banach space and A a closed standard operator algebra on X. Then every local automorphism of A is an automorphism. The assumptions of infinite-dimensionality, separability, and closeness are all indispensable.     

STABILITY AND SUPERSTABILITY OF JORDAN HOMOMORPHISMS AND JORDAN DERIVATIONS ON BANACH ALGEBRAS AND C~＊-ALGEBRAS： A FIXED POINT APPROACH

Using fixed point methods, we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equationwhere r is a fixed positive real number in (1, ∞).     

Convexoid and generalized derivations

Let E,F be two Banach spaces and let S be a symmetric norm ideal of L(E,F). For AL(F) and BL(E) the generalized derivation δ_S,A,B is the operator on S that sends X to AX−XB. A bounded linear operator is said to be convexoid if its (algebraic) numerical range coincides with the convex hull of its spectrum. We show that δ_S,A,B is convexoid if and only if A and B are convexoid.     

On approximately higher ring derivations

In this paper, we examine the Hyers-Ulam, the Isac and Rassias-type stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation, respectively:

     

三角代数上的广义Jordan导子

主要研究了三角代数上的广义Jordan导子．利用三角代数上广义Jordan导子和广义内导子的联系．证明了作用在一个含单位元的可交换环上的三角代数到其自身上的环线性广义Jordan导子是一个广义导子．     

Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G.     

A note on depth-first derivations

It is shown that the depth-first Szilard language associated with the depth-first derivations of a context-free grammar is ans-language.This work was supported by the Academy of Finland.     

Characterizations of isomorphisms and derivations of some algebras

Let ? be a zero-product preserving bijective bounded linear map from a unital algebra A onto a unital algebra B such that ?(1)=k. We show that if A is a CSL algebra on a Hilbert space or a J-lattice algebra on a Banach space then there exists an isomorphism ψ from A onto B such that ?=kψ. For a nest algebra A in a factor von Neumann algebra, we characterize the linear maps on A such that δ(x)y+xδ(y)=0 for all x,y∈A with xy=0.     

M_2(R)上的非线性Lie导子

设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和.