On the behaviour of Jordan-algebra norms on associative algebras

Miguel Cabrera Garcia; Antonio Moreno Galindo; Angel Rodríguez Palacios

Studia Mathematica (1995)

  • Volume: 113, Issue: 1, page 81-100
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Cabrera Garcia, Miguel, Moreno Galindo, Antonio, and Rodríguez Palacios, Angel. "On the behaviour of Jordan-algebra norms on associative algebras." Studia Mathematica 113.1 (1995): 81-100. <http://eudml.org/doc/216162>.

@article{CabreraGarcia1995,
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.},
author = {Cabrera Garcia, Miguel, Moreno Galindo, Antonio, Rodríguez Palacios, Angel},
journal = {Studia Mathematica},
keywords = {semiprime algebra; simple algebra; normed Jordan algebras; Jordan product},
language = {eng},
number = {1},
pages = {81-100},
title = {On the behaviour of Jordan-algebra norms on associative algebras},
url = {http://eudml.org/doc/216162},
volume = {113},
year = {1995},
}

TY - JOUR
AU - Cabrera Garcia, Miguel
AU - Moreno Galindo, Antonio
AU - Rodríguez Palacios, Angel
TI - On the behaviour of Jordan-algebra norms on associative algebras
JO - Studia Mathematica
PY - 1995
VL - 113
IS - 1
SP - 81
EP - 100
AB - 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.
LA - eng
KW - semiprime algebra; simple algebra; normed Jordan algebras; Jordan product
UR - http://eudml.org/doc/216162
ER -

References

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