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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Algebras with unconditional orthogonal bases


Authors: Taqdir Husain and Saleem Watson
Journal: Proc. Amer. Math. Soc. 79 (1980), 539-545
MSC: Primary 46H10
MathSciNet review: 572297
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Abstract: This is a continuation of our study of topological algebras with orthogonal Schauder bases. In the previous paper, the structure of closed ideals was determined and it was shown that the closed-maximal ideal space is homeomorphic with the discrete space of positive integers. Here it is shown that the space of all maximal ideals equipped with the hull-kernel topology is homeomorphic with the Stone-Čech compactification of natural numbers. Among other results it is also proved that the intersection of dense maximal ideals is isomorphic with the topological dual of the algebra under certain conditions.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0572297-6
PII: S 0002-9939(1980)0572297-6
Keywords: Topological algebras, orthogonal Schauder bases, maximal ideal space
Article copyright: © Copyright 1980 American Mathematical Society