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.

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.

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

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 x be a banach space of dimx > 2 and b(x) be the space of bounded linear operators on x. if l : b(x) → b(x) be a lie higher derivation on b(x), then there exists an additive higher derivation d and a linear map τ : b(x) → fi vanishing at commutators [a, b] for all a, b ∈ b(x) such that l = d + τ

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$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$