Jiankui Li

Characterizations of Jordan derivations and Jordan homomorphisms

Let 𝒜 be a unital Banach algebra and ℳ be a unital 𝒜-bimodule. We show that if δ is a linear mapping from 𝒜 into ℳ satisfying δ(ST) = δ(S)T +Sδ(T) for any S, T ∈ 𝒜 with ST = W, where W is a left or right separating point of ℳ, then δ is a Jordan derivation. Also, it is shown that every linear mapping h from 𝒜 into a unital Banach algebra ℬ which satisfies h(S)h(T) = h(ST) for any S, T ∈ 𝒜 with ST = W is a Jordan homomorphism if h(W) is a separating point of ℬ.

CHARACTERIZATIONS OF LIE HIGHER AND LIE TRIPLE DERIVATIONS ON TRIANGULAR ALGEBRAS

In this paper, we show that under certain conditions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively. The main results are then applied to (block) upper triangular matrix algebras and nest algebras.

Algebraic reflexivity of linear transformations

Let L(U, V) be the set of all linear transformations from U to V, where U and V are vector spaces over a field F. We show that every n-dimensional subspace of L(U, V) is algebraically [√2n]-reflexive, where [ t ] denotes the largest integer not exceeding t, provided n is less than the cardinality of F.

Jordan and Jordan higher all-derivable points of some algebras

In this article, we characterize Jordan derivable mappings in terms of the Peirce decomposition and determine Jordan all-derivable points for some general bimodules. Then we generalize the results to the case of Jordan higher derivable mappings. An immediate application of our main results shows that for a nest 𝒩 on a Banach space X with the associated nest algebra alg 𝒩, if there exists a non-trivial element in 𝒩 that is complemented in X, then every C ∈ alg 𝒩 is a Jordan all-derivable point of L(alg 𝒩, B(X)) and a Jordan higher all-derivable point of L(alg 𝒩).

Characterizations of linear mappings through zero products or zero Jordan products

Let

Characterizations of Jordan derivations on strongly double triangle subspace lattice algebras

\mathcal{A}

Algebraic isomorphisms and J-subspace lattices

be a unital

On (m,n)-Derivations of Some Algebras

*

DERIVATIONS OF CERTAIN OPERATOR ALGEBRAS

-algebra and

Characterizations of Jordan mappings on some rings and algebras through zero products

\mathcal{M}