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Commensurate sequences of characters


Author: A. Pełczyński
Journal: Proc. Amer. Math. Soc. 104 (1988), 525-531
MSC: Primary 43A15; Secondary 43A46, 46B15
MathSciNet review: 962823
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Abstract: If $ ({a_j})$ and $ ({b_j})$ are sequences of characters on compact abelian groups $ S$ and $ T$ respectively such that for every sequence of scalars $ ({\alpha _j})\vert\vert\sum {\alpha _j}{a_j}\vert{\vert _\infty } \asymp \vert\vert\sum {\alpha _j}{b_j}\vert{\vert _\infty }$ tnen for every $ 1 \leq p < \infty $ and every sequence $ ({x_j})$ of elements of an arbitrary Banach space $ X$

$\displaystyle {\int_S {\left\Vert {\sum {{x_j}{a_j}} } \right\Vert} ^p}ds \asymp {\int_T {\left\Vert {\sum {{x_j}b} } \right\Vert} ^p}dt.$

This result generalizes a result of Pisier [Pi 1] for Sidon sets. For topological Sidon sets on $ {\mathbf{R}}$ a slightly stronger result holds.

References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0962823-4
Keywords: Commensurate sequences, Sidon sets
Article copyright: © Copyright 1988 American Mathematical Society