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 ...

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 ...

let $mathcal m$ be a factor von neumann algebra. it is shown that every nonlinear $*$-lie higher derivation$d={phi_{n}}_{ninmathbb{n}}$ on $mathcal m$ is additive. in particular, if $mathcal m$ is infinite type $i$factor, a concrete characterization of $d$ is given.

After introducing double derivations of $n$-Lie algebra $L$ we‎ ‎describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual‎ ‎derivation Lie algebra $mathcal Der(L)$‎. ‎In particular‎, ‎we prove that the inner derivation algebra $ad(L)$‎ ‎is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra‎ ‎wit...

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...

using fixed pointmethods, we investigate approximately higher ternary jordan derivations in banach ternaty algebras via the cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$