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Isomorphisms of H*-algebras

Published online by Cambridge University Press:  24 October 2008

Jose Antonio Cuenca Mira  and
Angel Rodriguez Palacios
Jose Antonio Cuenca Mira
Affiliation:
Departamento de Algebra y Fundamentos, Universidad de Málaga, Spain
Angel Rodriguez Palacios
Affiliation:
Departamento de Teoría de Funciones, Universidad de Granada, Spain
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Extract

H*-algebras were introduced and studied by Ambrose [1] in the associative case, and the theory has been extended to such particular classes of non-associative algebras as Lie [18, 19], Jordan[20, 21, 7], alternative [11] and non-commutative Jordan [6] algebras. In all these cases the core of the matter is showing that every H*-algebra (in the given class) with zero annihilator is the closure of the orthogonal sum of its minimal closed ideals (each of which is a topologically simple H*-algebra), and then listing all the topologically simple H*-algebras in the class. In fact every nonassociative H*-algebra with zero annihilator is the closure of the orthogonal sum of its minimal closed ideals [6, theorem 2·7], so the problem of the classification of topologically simple non-associative H*-algebras becomes interesting. In relation with this problem the question arises whether, once an algebra A has been structured as a topologically simple H*-algebra, every H*-algebra structure on A is (up to a positive multiple of the inner product) totally isomorphic to the given one (see [3] and [11, section 4]). As a consequence of the results in this paper we give a general affirmative answer to this question.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 1 , January 1985 , pp. 93 - 99
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

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