On a conjecture concerning some automatic continuity theorems

Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Φ be an injective homomorphism from  A to  B . Under additional assumptions, we characterize the continuity of the homomorphism Φ −1 /Im Φ by the fact that the radical (or strong radic...

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Bibliographic Details
Published in:Rendiconti del Circolo matematico di Palermo 2012-04, Vol.61 (1), p.13-17
Main Author: El Azhari, M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Functional Analysis
Geometry
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
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Summary:Let A and B be commutative locally convex algebras with unit. A is assumed to be a uniform topological algebra. Let Φ be an injective homomorphism from  A to  B . Under additional assumptions, we characterize the continuity of the homomorphism Φ −1 /Im Φ by the fact that the radical (or strong radical) of the closure of Im Φ has only zero as a common point with Im Φ. This gives an answer to a conjecture concerning some automatic continuity theorems on uniform topological algebras.
ISSN:0009-725X
1973-4409
DOI:10.1007/s12215-011-0070-2