Polynomial identities of Banach algebras

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• 作者：L. Cioletti ; J. A. Freitas ; D. J. Gonçalves
• 关键词：PI ; algebras ; Normed algebras ; Banach algebras
• 刊名：Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：58
• 期：1
• 页码：189-194
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algebra; Geometry; Algebraic Geometry; Convex and Discrete Geometry;
• 出版者：Springer Berlin Heidelberg
• ISSN：2191-0383
• 卷排序：58

文摘

In this paper we consider PI-algebras A over the real and complex numbers and address the question of whether it is possible to find a normed PI-algebra B with the same polynomial identities as A, and moreover, whether there is some Banach PI-algebra with this property. Our main theorem provides an affirmative answer for this question and moreover we also show the existence of a Banach Algebra with the same polynomial identities as A. As a byproduct we prove that if A is a normed PI-algebra and its completion is nil, then A is nilpotent.