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

 

Subalgebras of $ L\sb{\infty }$ of the circle group


Author: Leon Brown
Journal: Proc. Amer. Math. Soc. 25 (1970), 585-587
MSC: Primary 42.56; Secondary 46.00
MathSciNet review: 0259501
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Abstract: In this note, we prove a theorem about subalgebras of a Banach algebra. Thus a theorem of J. P. Kahane and Y. Katznelson implies a theorem of R. Salem and these theorems imply that a number of subspaces of $ {L_\infty }$ of the circle group are not algebras.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0259501-2
PII: S 0002-9939(1970)0259501-2
Keywords: Subalgebra, uniform convergence, Fourier series
Article copyright: © Copyright 1970 American Mathematical Society