| Title:
|
An identity with generalized derivations on Lie ideals, right ideals and Banach algebras (English) |
| Author:
|
de Filippis, Vincenzo |
| Author:
|
Scudo, Giovanni |
| Author:
|
Tammam El-Sayiad, Mohammad S. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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62 |
| Issue:
|
2 |
| Year:
|
2012 |
| Pages:
|
453-468 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a prime ring of characteristic different from $2$, $U$ the Utumi quotient ring of $R$, $C=Z(U)$ the extended centroid of $R$, $L$ a non-central Lie ideal of $R$, $F$ a non-zero generalized derivation of $R$. Suppose that $[F(u),u]F(u)=0$ for all $u\in L$, then one of the following holds: (1) there exists $\alpha \in C$ such that $F(x)=\alpha x$ for all $x\in R$; (2) $R$ satisfies the standard identity $s_4$ and there exist $a\in U$ and $\alpha \in C$ such that $F(x)=ax+xa+\alpha x$ for all $x\in R$. We also extend the result to the one-sided case. Finally, as an application we obtain some range inclusion results of continuous or spectrally bounded generalized derivations on Banach algebras. (English) |
| Keyword:
|
prime rings |
| Keyword:
|
differential identities |
| Keyword:
|
generalized derivations |
| Keyword:
|
Banach algebra |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| MSC:
|
47B47 |
| MSC:
|
47B48 |
| idZBL:
|
Zbl 1249.16045 |
| idMR:
|
MR2990186 |
| DOI:
|
10.1007/s10587-012-0039-0 |
| . |
| Date available:
|
2012-06-08T09:45:01Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142838 |
| . |
| Reference:
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