Subalgebras of $L_{\infty }$ of the circle group
Author:
Leon Brown
Journal:
Proc. Amer. Math. Soc. 25 (1970), 585-587
MSC:
Primary 42.56; Secondary 46.00
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259501-2
MathSciNet review:
0259501
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Abstract | References | Similar Articles | Additional Information
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.
- Jean-Pierre Kahane and Yitzhak Katznelson, Sur les séries de Fourier uniformément convergentes, C. R. Acad. Sci. Paris 261 (1965), 3025–3028 (French). MR 188695
- R. Salem, A singularity of the Fourier series of continuous functions, Duke Math. J. 10 (1943), 711–716. MR 9220
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Keywords:
Subalgebra,
uniform convergence,
Fourier series
Article copyright:
© Copyright 1970
American Mathematical Society