Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

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

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences