Let $mathfrak{A}$ be a Banach algebra. We say that a sequence ${D_n}_{n=0}^infty$ of continuous operators form $mathfrak{A}$ into $mathfrak{A}$ is a textit{local higher derivation} if to each $ainmathfrak{A}$ there corresponds a continuous higher derivation ${d_{a,n}}_{n=0}^infty$ such that $D_n(a)=d_{a,n}(a)$ for each non-negative integer $n$. We show that if $mathfrak{A}$ is a $C^*$-algebra t...

We prove that every 2-local derivation from the algebra Mn(A)(n > 2) into its bimodule Mn(M) is a derivation, where A is a unital Banach algebra and M is a unital A-bimodule such that each Jordan derivation from A into M is an inner derivation, and that every 2-local derivation on a C*-algebra with a faithful traceable representation is a derivation. We also characterize local and 2-local Lie d...

let  be a banach algebra. let  be linear mappings on . first we demonstrate a theorem concerning the continuity of double derivations; especially that all of -double derivations are continuous on semi-simple banach algebras, in certain case. afterwards we define a new vocabulary called “-higher double derivation” and present a relation between this subject and derivations and finally give some ...

We characterize derivations and 2-local derivations from Mn(A) into Mn(M), n ≥ 2, where A is a unital algebra over C and M is a unital A-bimodule. We show that every derivation D : Mn(A) → Mn(M), n ≥ 2, is the sum of an inner derivation and a derivation induced by a derivation from A to M. We say that A commutes with M if am = ma for every a ∈ A and m ∈ M. If A commutes with M we prove that eve...

Wrappers export the schema and data of existing heterogeneous databases and support queries on them. In the context of cooperative information systems, we present a exible approach to specify the derivation of object-oriented export databases from local relational databases. Our export database derivation consists of a set of extent derivation structures which de-nes the extent and deep extent ...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

let a be a unital r-algebra and m be a unital a-bimodule. it is shown that every jordan derivation of the trivial extension of a by m, under some conditions, is the sum of a derivation and an antiderivation.