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A short computation of the norms of free convolution operators


Author: Wolfgang Woess
Journal: Proc. Amer. Math. Soc. 96 (1986), 167-170
MSC: Primary 43A05; Secondary 43A15
DOI: https://doi.org/10.1090/S0002-9939-1986-0813831-3
MathSciNet review: 813831
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Abstract: Akemann and Ostrand in 1976 gave a formula for the norms of free convolution operators on the $ {L^2}$-space of a discrete group. Using random walk techniques and generating functions, a short and elementary computation of this formula is given.


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

  • [1] Ch. A. Akemann and Ph. A. Ostrand, Computing norms in group $ {C^*}$-algebras, Amer. J. Math. 98 (1976), 1015-1047. MR 0442698 (56:1079)
  • [2] Ch. Berg and J. P. R. Christensen, Sur la norme des opérateurs de convolution, Invent. Math. 23 (1974), 173-178. MR 0338685 (49:3449)
  • [3] P. Gerl and W. Woess, Local limits and harmonic functions for nonisotropic random walks on free groups, Z. Wahrsch. Verw. Gebiete (to appear). MR 824708 (87m:60055)
  • [4] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. MR 0109367 (22:253)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0813831-3
Keywords: Norm of a convolution operator, Leinert property, free group, alternating random walk
Article copyright: © Copyright 1986 American Mathematical Society

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