Approximate diagonals and Følner conditions for amenable group and semigroup algebras

Studia Mathematica

Volumn 164, Issue 2, 2004, Pages 139-159

  Stokke, Ross ^a,b  

^a University of Winnipeg ^*

^b UNIVERSITY OF WINNIPEG   (Canada)

Author keywords

Amenability; Approximate diagonal; F lner conditions; Group algebra; Locally compact group; Semigroup algebra; Virtual diagonal

Indexed keywords

EID: 3242803647     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm164-2-3     Document Type: Article

References (24)

1. A. H. Clifford and G. B. Preston, The. Algebraic Theory of Semigroups I, Math. Surveys 7, Amer. Math. Soc., Providence, RI, 1961.
2. G. Corach and J. E. Galé, On amenability and geometry of spaces of bounded representations, J. London Math. Soc. (2) 59 (1999), 311-329.
3. H. G. Dales, Banach Algebras and Automatic Continuity, Oxford Univ. Press, 2001.
4. J. Duncan and I. Namioka, Amenability of inverse semigroups and their semigroup algebras, Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 309-321.
5. J. Duncan and A. L. T. Paterson, Amenability for discrete convolution semigroup algebras, Math. Scand. 66 (1990), 141-146.
6. G. H. Esslamzadeh, Banach algebra structure and amenability of a class of matrix algebras with applications, J. Funct. Anal. 161 (1999), 364-383.
7. E. Følner, On groups with full Banach mean values, Math. Scand. 3 (1955), 243-254.
8. F. P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand, New York, 1969.
9. N. Grønbæk, Amenability of weighted discrete convolution algebras on cancellative semigroups, Proc. Roy. Soc. Edinburgh Sect. A 110 (1988), 351-360.
10. _, Amenability of discrete convolution algebras, the commutative case, Pacific J. Math. 143 (1990), 243-249.
11. _, Various notions of amenability, a survey of problems, in: E. Albrecht and M. Mathieu (eds.), Banach Algebras'97, de Gruyter, Berlin, 1998, 535-548.
12. E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Springer, New York, 1963.
13. B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
14. _, Approximate diagonals and cohomology of certain annihilator Banach algebras, Amer. J. Math, 94 (1972), 685-698.
15. _, Weak amenability of group algebras, Bull. London Math. Soc. 23 (1991), 281-284.
16. A. T.-M. Lau and R. J. Loy, Amenability of convolution algebras, Math. Scand. 79 (1996), 283-296.
17. V. Losert and H. Rindler, Asymptotically central functions and invariant extensions of Dirac measure, in: Probability Measures on Groups VII (Oberwolfach, 1983), Lecture Notes in Math. 1064, Springer, Berlin, 1984, 368-378.
18. I. Namioka, Følner conditions for amenable semigroups, Math. Scand. 15 (1964), 18-28.
19. A. L. T. Paterson, Amenability, Amer. Math. Soc., Providence, RI, 1988.
20. J. P. Pier, Amenable Locally Compact Groups, Wiley, New York, 1984.
21. V. Runde, Lectures on Amenability, Lecture Notes in Math. 1774, Springer, Berlin, 2002.
22. R. Stokke, Quasi-central bounded approximate identities in group algebras of locally compact groups, Illinois J. Math. 48 (2004), 151-170.
23. Z. Yang, Følner numbers and Følner type conditions for amenable semigroups, ibid. 31 (1987), 496-517.
24. Y. Zhang, Approximate complementation and its applications in. studying ideals of Banach algebras, Math, Scand. 92 (2003), 301-308.