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Title

On the behaviour of Jordan-algebra norms on associative algebras

Authors 1, 1, 1

Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract

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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Studia Mathematica
1995/113/1
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Pages:
81-100
Main language of publication
English
Received
1994-06-10
Accepted
1994-09-26
Published
1995
Exact and natural sciences