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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On trigonometric series associated with separable, translation invariant subspaces of $ L\sp{\infty }(G)$


Author: Ron C. Blei
Journal: Trans. Amer. Math. Soc. 173 (1972), 491-499
MSC: Primary 43A25
MathSciNet review: 0313715
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Abstract: $ G$ denotes a compact abelian group, and $ \Gamma $ denotes its dual. Our main result is that every non-Sidon set $ E \subset \Gamma $ contains a non-Sidon set $ F$ such that $ L_F^\infty (G) = { \oplus _l}1_{i = 1}^\infty {C_{{F_i}}}(G)$, where the $ {F_i}$'s are finite, mutually disjoint, and $ \cup _{i = 1}^\infty {F_i} = F$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0313715-8
PII: S 0002-9947(1972)0313715-8
Keywords: Sidon set, Helson set, sup-norm partition
Article copyright: © Copyright 1972 American Mathematical Society