Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0957.46032
Villena, A.R.
Lie derivations on Banach algebras. (English)
[J] J. Algebra 226, No.1, 390-409 (2000). ISSN 0021-8693

A Lie derivation $\Delta$ on a unital complex Banach algebra $A$ is considered. The main result of the article is the following\par Theorem. Let $D$ be a Lie derivation on a unital complex Banach algebra $A$. Then for every primitive ideal $P$ of $A$, except for a finite set of them which have finite codimension greater than one, there exist a derivation $d$ from $A/P$ to itself and a linear functional $\tau$ on $A$ such that $$Q_p\Delta(a)= d(a+ P)+ \tau(a)$$ for all $a\in A$ (where $Q_p$ denotes the quotient map from $A$ onto $A(p)$.\par Moreover, the preceding decomposition holds for all primitive ideals in the case where $\Delta$ is continuous.
[Andreiy Kondrat'yev (Pensacola)]

MSC 2000:: *46H05 General theory of topological algebras

Keywords: Lie derivation; unital complex Banach algebra; primitive ideal

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]