Norms of free operators
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- by Massimo A. Picardello and Tadeusz Pytlik
- Proc. Amer. Math. Soc. 104 (1988), 257-261
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958078-7
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Abstract:
We give a short and elementary proof of the formula for the norm of a free convolution operator on ${L^2}$ of a discrete group. The formula was obtained in 1976 by C. Akemann and Ph. Ostrand, and by several other authors afterwards.References
- Charles A. Akemann and Phillip A. Ostrand, Computing norms in group $C^*$-algebras, Amer. J. Math. 98 (1976), no. 4, 1015–1047. MR 442698, DOI 10.2307/2374039
- Kazuhiko Aomoto, Spectral theory on a free group and algebraic curves, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 31 (1984), no. 2, 297–318. MR 763424
- Marek Bożejko, The existence of $\Lambda (p)$ sets in discrete noncommutative groups, Boll. Un. Mat. Ital. (4) 8 (1973), 579–582 (English, with Italian summary). MR 0344805
- P. Cartier, Fonctions harmoniques sur un arbre, Symposia Mathematica, Vol. IX (Convegno di Calcolo delle Probabilità & Convegno di Teoria della Turbolenza, INDAM, Rome, 1971) Academic Press, London, 1972, pp. 203–270 (French). MR 0353467
- Alessandro Figà-Talamanca and Massimo A. Picardello, Spherical functions and harmonic analysis on free groups, J. Functional Analysis 47 (1982), no. 3, 281–304. MR 665019, DOI 10.1016/0022-1236(82)90108-2 A. Figà-Talamanca and T. Steger, Harmonic analysis for anisotropic random walks on a homogeneous tree, Mem. Amer. Math. Soc. (in print).
- Uffe Haagerup, An example of a nonnuclear $C^{\ast }$-algebra, which has the metric approximation property, Invent. Math. 50 (1978/79), no. 3, 279–293. MR 520930, DOI 10.1007/BF01410082
- Harry Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336–354. MR 109367, DOI 10.1090/S0002-9947-1959-0109367-6
- Michael Leinert, Faltungsoperatoren auf gewissen diskreten Gruppen, Studia Math. 52 (1974), 149–158 (German). MR 355480, DOI 10.4064/sm-52-2-149-158
- T. Pytlik, Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. Reine Angew. Math. 326 (1981), 124–135. MR 622348, DOI 10.1515/crll.1981.326.124
- Tadeusz Pytlik, Radial convolutors on free groups, Studia Math. 78 (1984), no. 2, 179–183. MR 766714, DOI 10.4064/sm-78-2-179-183 T. Steger, Harmonic analysis for an anisotropic random walk on a homogeneous tree, Ph. D. dissertation, Washington University, 1985.
- Wolfgang Woess, A short computation of the norms of free convolution operators, Proc. Amer. Math. Soc. 96 (1986), no. 1, 167–170. MR 813831, DOI 10.1090/S0002-9939-1986-0813831-3
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 257-261
- MSC: Primary 47A30; Secondary 20E05, 43A15, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1988-0958078-7
- MathSciNet review: 958078