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, ∞).     

Some results on stability of extended derivations

In this paper we prove the generalized Hyers-Ulam-Rassias stability of extended derivations on unital Banach algebras associated to a generalized Jensen equation.     

A note on generalized derivations in Banach algebras

In this note we characterize a complex Banach algebra A admitting a generalized derivation g such that the cardinality of the spectrum σ(g(x)) is exactly one for all x∈A.     

Banach代数上的高阶Jordan-triple导子系的广义Hyers-Ulam-Rassias稳定性

针对Banach代数上的高阶Jordan—triple导子系,基于与函数方程有关的广义的Hyers—Ulam-Rassias稳定性的原理．采用线性算子论的方法,结合广义的Jensen等式,证明了Banach代数上与高阶导子系有关的函数方程具有广义的Hyers—Ulam-Rassias稳定性．证明结果表明该方法实用性强,...     

Local derivations of reflexive algebras

Let be a reflexive algebra in Banach space such that both and in , the invariant subspace lattice of , then every derivation of into itself is spatial. Furthermore, if is additionally reflexive, then the set of all inner derivations of into itself is topologically algebraically reflexive.

     

A characterization of generalized derivations of JSL algebras

Let AlgL be a J-subspace lattice algebra on a Banach space X and M be an operator in AlgL. We prove that if δ : AlgL → B(X) is a linear mapping satisfying δ(AB) = δ(A)B + Aδ(B)for all A, B ∈ AlgL with AMB = 0, then δ is a generalized derivation. This result can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.     

Jordan generalized derivations on triangular algebras

Let 𝒜 be a unital algebra and let ? be a unitary 𝒜-bimodule. We consider Jordan generalized derivations mapping from 𝒜 into ?. Our results on unitary algebras are applied to triangular algebras. In particular, we prove that any Jordan generalized derivation of a triangular algebra is a generalized derivation.     

Local derivations of reflexive algebras II

Let be a reflexive algebra in Banach space such that both and in Lat . Then every local derivation of into itself is a derivation.

     

Bilocal derivations of standard operator algebras

In this paper, we shall show the following two results: (1) Let be a standard operator algebra with , if is a linear mapping on which satisfies that maps into for all , then is of the form for some in . (2) Let be a Hilbert space, if is a norm-continuous linear mapping on which satisfies that maps into for all self-adjoint projection in , then is of the form for some in .

     

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．     

A note on the stability of Jordan triple higher ring derivations

In the present paper, we establish the stability and the superstability of a functional inequality corresponding to the functional equation fn（xyx） = ∑i＋j＋k=n fi（x）fj （y）fk（x）. In addition, we take account of the problem of Jacobson radical ranges for such functional inequality.     

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: