On the spectrum of the sum of generators of a finitely generated group, II

Pierre de la Harpe; A. Robertson; Alain Valette

Colloquium Mathematicae (1993)

  • Volume: 65, Issue: 1, page 87-102
  • ISSN: 0010-1354

How to cite


de la Harpe, Pierre, Robertson, A., and Valette, Alain. "On the spectrum of the sum of generators of a finitely generated group, II." Colloquium Mathematicae 65.1 (1993): 87-102. <http://eudml.org/doc/210209>.

author = {de la Harpe, Pierre, Robertson, A., Valette, Alain},
journal = {Colloquium Mathematicae},
keywords = {finitely generated group; full -algebra; reduced -algebra; left regular representation; spectrum; representation theory},
language = {eng},
number = {1},
pages = {87-102},
title = {On the spectrum of the sum of generators of a finitely generated group, II},
url = {http://eudml.org/doc/210209},
volume = {65},
year = {1993},

AU - de la Harpe, Pierre
AU - Robertson, A.
AU - Valette, Alain
TI - On the spectrum of the sum of generators of a finitely generated group, II
JO - Colloquium Mathematicae
PY - 1993
VL - 65
IS - 1
SP - 87
EP - 102
LA - eng
KW - finitely generated group; full -algebra; reduced -algebra; left regular representation; spectrum; representation theory
UR - http://eudml.org/doc/210209
ER -


  1. [AkO] C. A. Akemann and P. A. Ostrand, Computing norms in group C*-algebras, Amer. J. Math. 98 (1976), 1015-1047. Zbl0342.22008
  2. [Ber] S. K. Berberian, Trace and the convex hull of the spectrum in a von Neumann algebra of finite class, Proc. Amer. Math. Soc. 23 (1969), 211-212. Zbl0182.17804
  3. [BeC] C. Berg and J. P. R. Christensen, On the relation between amenability of locally compact groups and the norms of convolution operators, Math. Ann. 208 (1974), 149-153. Zbl0264.43003
  4. [Bro] L. Brown, Lidskii's theorem in the type II case, in: Geometric Methods in Operator Algebras, H. Araki and E. G. Effros (eds.), Pitman Res. Notes in Math. Ser. 123, Longman, 1986, 1-35. 
  5. [Day] M. M. Day, Convolutions, means and spectra, Illinois J. Math. 8 (1964), 100-111. Zbl0122.11703
  6. [DeG] Y. Derriennic et Y. Guivarc'h, Théorème de renouvellement pour les groupes non moyennables, C. R. Acad. Sci. Paris 277 (1973), 613-615. Zbl0272.60005
  7. [DuS] N. Dunford and J. T. Schwartz, Linear Operators, Interscience, 1958. 
  8. [Fac] T. Fack, Sur la notion de valeur caractéristique, J. Operator Theory 7 (1982), 307-333. Zbl0493.46052
  9. [Far] J. Faraut, Moyennabilité et normes d'opérateurs de convolution, in: Analyse harmonique sur les groupes de Lie (Sém. Nancy-Strasbourg 1973-75), Lecture Notes in Math. 497, Springer, 1975, 153-163. 
  10. [For] E. Formanek, A problem of Herstein on group rings, Canad. Math. Bull. 17 (1974), 201-202. Zbl0291.16009
  11. [Haa] U. Haagerup, An example of a non-nuclear C*-algebra which has the metric approximation property, Invent. Math. 50 (1979), 279-293. Zbl0408.46046
  12. [Har] F. Harary, Graph Theory, Addison-Wesley, 1972. 
  13. [dHa] P. de la Harpe, Groupes hyperboliques, algèbres d'opérateurs et un théorème de Jolissaint, C. R. Acad. Sci. Paris (Sér. I) 307 (1988), 771-774. Zbl0653.46059
  14. [HRV] P. de la Harpe, A. G. Robertson and A. Valette, On the spectrum of the sum of generators of a finitely generated group, Israel J. Math., to appear. Zbl0846.46036
  15. [HaV] P. de la Harpe et A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175 (1989). 
  16. [Jol] P. Jolissaint, Rapidly decreasing functions in reduced C*-algebras of groups, Trans. Amer. Math. Soc. 317 (1990), 167-196. Zbl0711.46054
  17. [JoV] P. Jolissaint et A. Valette, Normes de Sobolev et convoluteurs bornés sur L 2 ( G ) , Ann. Inst. Fourier (Grenoble) 41 (1991), 797-822. Zbl0734.43002
  18. [KaW] M. A. Kaashoek and T. T. West, Locally compact monothetic semi-algebras, Proc. London Math. Soc. 18 (1968), 428-438. Zbl0162.18601
  19. [KaR] R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator Algebras I-II, Academic Press, 1983-1986. 
  20. [Kas] G. G. Kasparov, Lorentz groups: K-theory of unitary representations and crossed products, Dokl. Akad. Nauk SSSR 275 (1984), 541-545 (in Russian). 
  21. [Ke1] H. Kesten, Symmetric random walks on groups, Trans. Amer. Math. Soc. 92 (1959), 336-354. Zbl0092.33503
  22. [Ke2] H. Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959), 146-156. Zbl0092.26704
  23. [MoW] B. Mohar and W. Woess, A survey on spectra of infinite graphs, Bull. London Math. Soc. 21 (1989), 209-234. 
  24. [Ped] G. K. Pedersen, C*-Algebras and Their Automorphism Groups, Academic Press, 1979. 
  25. [PiV] M. Pimsner and D. Voiculescu, K-groups of reduced crossed products by free groups, J. Operator Theory 8 (1982), 131-156. Zbl0533.46045
  26. [RiN] F. Riesz et B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Gauthier-Villars, Paris 1955. Zbl0064.35404
  27. [Ros] J. M. Rosenblatt, Invariant measures and growth conditions, Trans. Amer. Math. Soc. 193 (1974), 33-53. Zbl0246.28017
  28. [Sch] H. H. Schaefer, Topological Vector Spaces, Graduate Texts in Math. 3, Springer, 1971. 
  29. [Str] S. P. Strunkov, On the spectrum of sums of generators of a finite group, Math. USSR-Izv. 37 (1991), 461-463. 
  30. [Val] A. Valette, Minimal projections, integrable representations and property (T), Arch. Math. (Basel) 43 (1984), 397-406. Zbl0538.22006
  31. [Woe] W. Woess, A short computation of the norms of free convolution operators, Proc. Amer. Math. Soc. 96 (1986), 167-170. Zbl0599.43007

Citations in EuDML Documents

  1. Pierre-Alain Cherix, Generic result for the existence of a free semi-group
  2. Donald I. Cartwright, Wojciech Młotkowski, Tim Steger, Property (T) and A ¯ 2 groups
  3. Pierre de la Harpe, A. Robertson, Alain Valette, On the spectrum of the sum of generators of a finitely generated group, II
  4. Alain Valette, On the Haagerup inequality and groups acting on A ˜ n -buildings
  5. Yehuda Shalom, Explicit Kazhdan constants for representations of semisimple and arithmetic groups
  6. Yehuda Shalom, Bounded generation and Kazhdan’s property ( T )

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.