We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these results and the normed versions of Zel'manov's prime theorem for Jordan algebras are discussed.
@article{bwmeta1.element.bwnjournal-article-smv113i1p81bwm,
author = {Miguel Cabrera Garcia and Antonio Moreno Galindo and Angel Rodr\'\i guez Palacios},
title = {On the behaviour of Jordan-algebra norms on associative algebras},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {81-100},
zbl = {0826.17038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p81bwm}
}
Cabrera Garcia, Miguel; Moreno Galindo, Antonio; Rodríguez Palacios, Angel. On the behaviour of Jordan-algebra norms on associative algebras. Studia Mathematica, Tome 113 (1995) pp. 81-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i1p81bwm/
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