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Structure theory for L*-algebras

Published online by Cambridge University Press:  24 October 2008

José Antonio Cuenca Mira ,
Amable García Martín  and
Cándido Martín González
José Antonio Cuenca Mira
Affiliation:
Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Apartado 59. 29080, Málaga, Spain
Amable García Martín
Affiliation:
Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Apartado 59. 29080, Málaga, Spain
Cándido Martín González
Affiliation:
Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Apartado 59. 29080, Málaga, Spain
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Abstract

The structure theory of separable complex L*-algebras was given by Schue in [10] and [11]. In [3] Balachandran makes a study of infinite-dimensional complex topologically simple L*-algebras of classical type and poses the question whether these algebras exhaust the class of all infinite-dimensional complex topologically simple L*-algebras. In this paper we give an affirmative answer by determining all the complex topologically simple infinite-dimensional L*-algebras. The case of the real L*-algebras was studied previously in [4], [9] and [12] also under the separability condition. Applying the result of Balachandran, our result yields the structure theory for real L*-algebras. The main tool used here is the ‘approximation’ of the L*-algebra by topologically simple separable L*-algebras via an ultraproduct construction.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 361 - 365
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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