On additivity of derivations

the structure of lie derivations on c*-algebras

نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.

On derivations of lattices

This de nition clearly coincides with the usual (algebraic) notion of derivation when [A; +, ·] is a ring. However, it can be formally stated for every algebraic structure endowed with two binary operations. In this paper, we will consider the special case in which [A; +, ·] is a lattice, so that + and · are, respectively, the join and the meet operations. These ideas have been introduced and d...

Remarks on Cyclic Additivity

Induction on Failing Derivations

A proof technique, called induction on failing derivations, is introduced. We wish to prove properties of judgments in deductive systems. Standard techniques exist for proving such properties on valid judgments; this note defines a technique for proving such properties on invalid (underivable) judgments.

Product of derivations on C$^*$-algebras

Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...