# 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

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topCabrera 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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## Citations in EuDML Documents

top- M. Cabrera Garcia, A. Moreno Galindo, A. Rodríguez Palacios, E. Zel'manov, Jordan polynomials can be analytically recognized
- A. Moreno Galindo, Distinguishing Jordan polynomials by means of a single Jordan-algebra norm
- A. Moreno Galindo, The triple-norm extension problem: the nondegenerate complete case.

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