Higher Derivations and Universal Differential Operators

Local higher derivations on C*-algebras are higher derivations

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...

Double Derivations, Higher Double Derivations and Automatic Continuity

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 ...

The characterization of differential operators by locality: abstract derivations

Let S be a closed *-derivation on a commutative C*-algebra M, suppose that ^ n = f l l = , D(8 ) is dense in si for some n = 1, 2 , . . . , oo, and let H:$4n^>si be a linear operator satisfying the locality condition supp(H/)cSupp(/), festn. It is shown that H =JJ p m=0 lm8 m on s£2m for some finite integer p<n and functions lm on X. Estimates on the coefficients lm are obtained and applied to ...

Prime Higher Derivations on Algebras

Higher Derivations and Field Extensions

Let K be a field having prime characteristic p. The following conditions on a subfield k of K are equivalent: (i) || K" (k) = k and K/k is separable, (ii) k is the field of constants of an infinite higher derivation defined in K. (iii) k is the field of constants of a set of infinite higher derivations defined in K. If K/k is separably generated and k is algebraically closed in K, then k is the...