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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Automatic continuity of homomorphisms in topological algebras


Author: S. J. Bhatt
Journal: Proc. Amer. Math. Soc. 119 (1993), 135-139
MSC: Primary 46H40; Secondary 46J40
DOI: https://doi.org/10.1090/S0002-9939-1993-1164140-0
MathSciNet review: 1164140
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Abstract: A homomorphism from a locally convex $ Q$-algebra to a uniform topological algebra is continuous. A one-to-one homomorphism from a regular complete spectrally bounded uniform topological algebra onto a dense subalgebra of a semisimple locally $ m$-convex $ Q$-algebra is open. Examples are discussed to show that none of the assumptions in these results can be omitted.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1164140-0
Keywords: Uniform seminorm, locally convex $ Q$-algebras, uniform algebras, regular algebras
Article copyright: © Copyright 1993 American Mathematical Society