# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Jordan $*$-derivation pairs on standard operator algebras and related results

### Tom 102 / 2005

Colloquium Mathematicum 102 (2005), 137-145 MSC: Primary 47B47; Secondary 39B52, 16W10. DOI: 10.4064/cm102-1-12

#### Streszczenie

Motivated by Problem 2 in \cite{mol1}, Jordan $*$-derivation pairs and $n$-Jordan $*$-mappings are studied. From the results on these mappings, an affirmative answer to Problem 2 in \cite{mol1} is given when $E=F$ in (1) or when $\mathcal{A}$ is unital. For the general case, we prove that every Jordan $*$-derivation pair is automatically real-linear. Furthermore, a characterization of a non-normal prime $*$-ring under some mild assumptions and a representation theorem for quasi-quadratic functionals are provided.

#### Autorzy

• Dilian YangDepartment of Pure Mathematics
University of Waterloo