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Totally multiplicatively prime algebras

Published online by Cambridge University Press:  12 July 2007

M. Cabrera  and
Amir A. Mohammed
M. Cabrera
Affiliation:
Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
Amir A. Mohammed
Affiliation:
Department of Mathematics, College of Education, University of Mosul, Mosul, Iraq
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Abstract

We introduce the totally multiplicatively prime algebras as those normed algebras for which there exists a positive number K such that K‖F‖‖a‖ ≤ ‖WF,a‖ for all F in M(A) (the multiplication algebra of A) and a in A, where WF,a denotes the operator from M(A) into A defined by WF,a(T) = FT(a) for all T in M(A). These algebras are totally prime and their multiplication algebra is ultraprime. We get the stability of the class of totally multiplicatively prime algebras by taking central closure. We prove that prime H*-algebras are totally multiplicatively prime and that the ℓ1-norm is the only classical norm on the free non-associative algebras for which these are totally multiplicatively prime.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 132 , Issue 5 , October 2002 , pp. 1145 - 1162
Copyright
Copyright © Royal Society of Edinburgh 2002

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