On the behaviour of Jordan-algebra norms on associative algebras
Studia Mathematica, Tome 113 (1995) no. 1, pp. 81-100
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
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author = {Miguel Cabrera Garcia and },
title = {On the behaviour of {Jordan-algebra} norms on associative algebras},
journal = {Studia Mathematica},
pages = {81--100},
publisher = {mathdoc},
volume = {113},
number = {1},
year = {1995},
doi = {10.4064/sm-113-1-81-100},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-113-1-81-100/}
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Miguel Cabrera Garcia; . On the behaviour of Jordan-algebra norms on associative algebras. Studia Mathematica, Tome 113 (1995) no. 1, pp. 81-100. doi: 10.4064/sm-113-1-81-100
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