Homomorphisms on infinite direct product algebras, especially Lie algebras

Families of Ultrafilters, and Homomorphisms on Infinite Direct Product Algebras

Criteria are obtained for a filter F of subsets of a set I to be an intersection of finitely many ultrafilters, respectively, finitely many κ-complete ultrafilters for a given uncountable cardinal κ. From these, general results are deduced concerning homomorphisms on infinite direct product groups, which yield quick proofs of some results in the literature: the Loś-Eda theorem (characterizing h...

Infinite-dimensional Lie algebras

Approximate n-Lie Homomorphisms and Jordan n-Lie Homomorphisms on n-Lie Algebras

and Applied Analysis 3 Park and Rassias 59 proved the stability of homomorphisms in C∗-algebras and Lie C∗-algebras and also of derivations on C∗-algebras and Lie C∗-algebras for the Jensen-type functional equation μf ( x y 2 ) μf ( x − y 2 ) − fμx 0 1.6 for all μ ∈ T1 : {λ ∈ C; |λ| 1}. In this paper, by using the fixed-point methods, we establish the stability of n-Lie homomorphisms and Jordan...

Lie $^*$-double derivations on Lie $C^*$-algebras

A unital $C^*$ -- algebra $mathcal A,$ endowed withthe Lie product $[x,y]=xy- yx$ on $mathcal A,$ is called a Lie$C^*$ -- algebra. Let $mathcal A$ be a Lie $C^*$ -- algebra and$g,h:mathcal A to mathcal A$ be $Bbb C$ -- linear mappings. A$Bbb C$ -- linear mapping $f:mathcal A to mathcal A$ is calleda Lie $(g,h)$ -- double derivation if$f([a,b])=[f(a),b]+[a,f(b)]+[g(a),h(b)]+[h(a),g(b)]$ for all ...

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.