Motivated by Problem 2 in [2], Jordan *-derivation pairs and n-Jordan *-mappings are studied. From the results on these mappings, an affirmative answer to Problem 2 in [2] is given when E = F in (1) or when 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-12,
author = {Dilian Yang},
title = {Jordan *-derivation pairs on standard operator algebras and related results},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {137-145},
zbl = {1087.47041},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-12}
}
Dilian Yang. Jordan *-derivation pairs on standard operator algebras and related results. Colloquium Mathematicae, Tome 103 (2005) pp. 137-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-1-12/