An elementary proof of a result on $\Lambda (p)$ sets
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- by Kathryn E. Hare
- Proc. Amer. Math. Soc. 104 (1988), 829-834
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964865-1
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Abstract:
We give an elementary proof of the fact that a subset of the dual of a compact abelian group which is a $\Lambda (p)$ set for some $1 \leq p < 2$ is a $\Lambda (p + \varepsilon )$ set for some $\varepsilon > 0$, and extend this result to $\Lambda (p)$ sets for $0 < p < 1$.References
- Gregory F. Bachelis and Samuel E. Ebenstein, On $\Lambda (p)$ sets, Pacific J. Math. 54 (1974), no. 1, 35–38. MR 383005, DOI 10.2140/pjm.1974.54.35
- Leonard E. Dor, On projections in $L_{1}$, Ann. of Math. (2) 102 (1975), no. 3, 463–474. MR 420244, DOI 10.2307/1971039
- Jorge M. López and Kenneth A. Ross, Sidon sets, Lecture Notes in Pure and Applied Mathematics, Vol. 13, Marcel Dekker, Inc., New York, 1975. MR 0440298 B. Maurey, Projections dans ${L^1}$, ’d’apres L. Dor’, is part of the title. Sem. Maurey-Schwartz 1974/75, #21.
- Haskell P. Rosenthal, On subspaces of $L^{p}$, Ann. of Math. (2) 97 (1973), 344–373. MR 312222, DOI 10.2307/1970850
- Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177, DOI 10.1512/iumj.1960.9.59013 N. Tomczak-Jaegermann, Finite-dimensional operator ideals and Banach-Mazur distances, Pitman, Boston, Mass. (to appear).
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 829-834
- MSC: Primary 43A46
- DOI: https://doi.org/10.1090/S0002-9939-1988-0964865-1
- MathSciNet review: 964865