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On the behaviour of Jordan-algebra norms on associative algebras

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Cabrera Garcia M., Galindo A. M., Palacios A. R.

Studia Mathematica

1995

tom 113

nr 1

81-100

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.

Ograniczanie wyników

1 Studia Mathematica

1 Cabrera Garcia M.

1 Galindo A. M.

1 Palacios A. R.

1 1995

Wyniki wyszukiwania

On the behaviour of Jordan-algebra norms on associative algebras