No CrossRef data available.
Article contents
A Non-abelian, Non-Sidon, Completely Bounded 
$\Lambda (p)$ Set
Published online by Cambridge University Press: 26 February 2020
Abstract
The purpose of this note is to construct an example of a discrete non-abelian group G and a subset E of G, not contained in any abelian subgroup, that is a completely bounded 
$\Lambda (p)$ set for all 
$p<\infty ,$ but is neither a Leinert set nor a weak Sidon set.
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2020
References
Bożejko, M., The existence of 
$\varLambda (p)$sets in discrete non-commutative groups. Boll. Un. Mat. Ital. 8(1973), 579–582.Google Scholar
$\varLambda (p)$sets in discrete non-commutative groups. Boll. Un. Mat. Ital. 8(1973), 579–582.Google ScholarBożejko, M., A remark to my paper: “The existence of $\varLambda (p)$sets in discrete noncommutative groups” (Boll. Un. Mat. Ital. 8(1973), 579–582). Boll. Un. Mat. Ital. 11(1975), 43.Google Scholar
$\varLambda (p)$sets in discrete noncommutative groups” (Boll. Un. Mat. Ital. 8(1973), 579–582). Boll. Un. Mat. Ital. 11(1975), 43.Google ScholarEymard, P., L’algèbre de Fourier d’un groupe localement compact. Bull. Soc. Math. France 92(1964), 181–236.Google Scholar
Figà-Talamanca, A. and Picardello, M., Multiplicateurs de $A(G)$qui ne sont pas dans $B(G)$. C. R. Acad. Sci. Paris Sér. A-B 277(1973), A117–A119.Google Scholar
$A(G)$qui ne sont pas dans 
$B(G)$. C. R. Acad. Sci. Paris Sér. A-B 277(1973), A117–A119.Google ScholarGraham, C. and Hare, K., Interpolation and Sidon sets in compact groups. CMS Books in Mathematics, Springer, New York, 2013. https://doi.org/10.1007/9781-4614-5392-5Google Scholar
Harcharras, A., Fourier analysis, Schur multipliers on ${S}^p$and non-commutative $\varLambda (p)$sets. Studia Math. 137(1999), 203–260. https://doi.org/10.4064/sm-137-3-203-260CrossRefGoogle Scholar
${S}^p$and non-commutative 
$\varLambda (p)$sets. Studia Math. 137(1999), 203–260. https://doi.org/10.4064/sm-137-3-203-260CrossRefGoogle ScholarHare, K. E. and Mohanty, P., Completely bounded $\varLambda (p)$sets that are not Sidon. Proc. Amer. Math. Soc. 144(2016), 2861–2869. https://doi.org/10.1090/proc/13039CrossRefGoogle Scholar
$\varLambda (p)$sets that are not Sidon. Proc. Amer. Math. Soc. 144(2016), 2861–2869. https://doi.org/10.1090/proc/13039CrossRefGoogle ScholarLeinert, M., Faltungsoperatoren auf gewissen diskreten Gruppen. Studia Math. 52(1974), 149–158. https://doi.org/10.4064/sm-52-2-149-158Google Scholar
López, J. and Ross, K., Sidon sets. Lecture Notes in Pure and Applied Mathematics, 13, Marcel Dekker, Inc., New York, 1975.Google Scholar
Picardello, M., Lacunary sets in discrete noncommutative groups. Boll. Un. Mat. Ital. 8(1973), 494–508.Google Scholar
Pisier, G., The operator Hilbert space $\mathrm{OH}$, complex interpolation and tensor norms. Mem. Amer. Math. Soc. 122(1996), no. 585. https://doi.org/10.1090/memo/0585CrossRefGoogle Scholar
$\mathrm{OH}$, complex interpolation and tensor norms. Mem. Amer. Math. Soc. 122(1996), no. 585. https://doi.org/10.1090/memo/0585CrossRefGoogle ScholarPisier, G. and Xu, Q., Non-commutative ${L}^p$-spaces. Handbook of the geometry of Banach spaces, 2, North-Holland, Amsterdam, 2003, pp. 1459–1517. https://doi.org/10.1016/S1874-5849(03)80041-4CrossRefGoogle Scholar
${L}^p$-spaces. Handbook of the geometry of Banach spaces, 2, North-Holland, Amsterdam, 2003, pp. 1459–1517. https://doi.org/10.1016/S1874-5849(03)80041-4CrossRefGoogle ScholarPisier, G., Multipliers and lacunary sets in non-amenable groups. Amer. J. Math. 117(1995), 337–376. https://doi.org/10.2307/2374918CrossRefGoogle Scholar
Popa, A.-M., On completely bounded multipliers of the Fourier algebra $A(G)$. Ph. D. thesis, University of Illinois at Urbana-Champaign. 2008.Google Scholar
$A(G)$. Ph. D. thesis, University of Illinois at Urbana-Champaign. 2008.Google ScholarRudin, W., Trigonometric series with gaps. J. Math. Mech. 9(1960), 203–227. https://doi.org/10.1512/iumj.1960.9.59013CrossRefGoogle Scholar
Wang, S., Lacunary Fourier series for compact quantum groups. Comm. Math. Phys. 349(2017), 895–945. https://doi.org/10.1007/s00220-016-2670-3CrossRefGoogle Scholar