Multipliers of uniform topological algebras

Let \(E\) be a complete uniform topological algebra with Arens-Michael normed factors \(\left(E_{\alpha}\right)_{\alpha\in\Lambda}.\) Then \(M\left(E\right) \cong \varprojlim M\left(E_{\alpha}\right)\) within an algebra isomorphism \(\varphi\). If each factor \(E_{\alpha}\) is complete, then every m...

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Bibliographic Details
Published in:arXiv.org 2017-01
Main Author: M El Azhari
Format: Article
Language:English
Subjects:
Algebra
Isomorphism
Topology
Online Access:Get full text
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Summary:Let \(E\) be a complete uniform topological algebra with Arens-Michael normed factors \(\left(E_{\alpha}\right)_{\alpha\in\Lambda}.\) Then \(M\left(E\right) \cong \varprojlim M\left(E_{\alpha}\right)\) within an algebra isomorphism \(\varphi\). If each factor \(E_{\alpha}\) is complete, then every multiplier of \(E\) is continuous and \(\varphi\) is a topological algebra isomorphism where \(M\left(E\right)\) is endowed with its seminorm topology.
ISSN:2331-8422
DOI:10.48550/arxiv.1608.05734