On the behaviour of Jordan-algebra norms on associative algebras
Tom 113 / 1995
Studia Mathematica 113 (1995), 81-100
DOI: 10.4064/sm-113-1-81-100
Streszczenie
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.
