Fixed point property and the fourier algebra of a locally compact group

Transactions of the American Mathematical Society

Volumn 360, Issue 12, 2008, Pages 6389-6402

  To Ming Lau, Anthony ^a   Leinert, Michael ^b  

^a UNIVERSITY OF ALBERTA   (Canada)

^b UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Fourier algebra; Noncommutative L1 space; Nonexpansive mapping; Semifinite von Neumann algebra; Weak fixed point property

Indexed keywords

EID: 70350589740     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-08-04622-9     Document Type: Article

References (37)

1. D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424. MR612733 (82j:47070)
2. L. Baggett and K. Taylor, Groups with completely reducible regular representation, Proceedings American Mathematical Society 72 (1978), 593-600. MR509261 (80b:22009)
3. T.D. Benavides, M.A. Japon Pineda and S. Prus, Weak compactness and fixed point property for affine maps, Journal of Functional Analysis 209 (2004), 1-15. MR2039215 (2005b:46046)
4. T.D. Benavides and M.A. Japon Pineda, Fixed points of nonexpansive mappings in spaces of continuous functions, AMS 133 (2005), 3037-3046. MR2159783 (2006d:47097)
5. R. Bourgin, Geometric aspects of convex sets with the Radon-Nikodym property,Lecture Notes in Math. 993, Springer-Verlag, Berlin, 1983. MR704815 (85d:46023)
6. M. Bozejko, Theexistenceof X(p) sets in discrete noncommutative groups, Boll. Un. Mat. Ital. (4) 8 (1973), 579-582. MR0344805 (49:9544)
7. F.E. Browder, Nonexpansive nonlinear operators in Banach spaces, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041-1044. MR0187120 (32:4574)
8. R.E. Bruck, A common fixed point theorem for a commutative family of nonexpansive mappings, Pacific Journal of Mathematics 53 (1974), 59-71. MR0361945 (50:14387)
9. C.H. Chu, A note on scattered C*-algebras and the Radon-Nikodym property, J. London Math. Soc. 24 (1981), 533-536. MR635884 (82k:46086)
10. J. Diestel and J.J. Uhl, Jr., Vector measures, Mathematical Survey 15, Amer. Math. Society, 1977. MR0453964 (56:12216)
11. J. Dixmier, C*-algebras, North-Holland Publishing Co., New York, 1977. MR0458185 (56:16388)
12. P.N. Dowling, C.J. Lennard and B. Turett, The fixed point property for subsets of some classical Banach spaces, Nonlinear Analysis, Theory, Methods and Applications 49 (2002), 141-145. MR1887917 (2002k:47115)
13. D. van Dulst and B. Sims, Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), p. 35-43 in: Lecture Notes in Math. (Banach space theory and its applications, Bucharest, 1981), vol. 991, Springer-Verlag, New York, 1983. MR714171 (84i:46027)
14. P. Eymard, L'algebre de Fourier d'un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181-236. MR0228628 (37:4208)
15. P.R. Halmos, Measure Theory, Van Nostrand, 1950. MR0033869 (11:504d)
16. E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, vol. I, Springer-Verlag, 1963. MR551496 (81k:43001)
17. R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749. MR595102 (82b:46016)
18. W.A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006. MR0189009 (32:6436)
19. W.A. Kirk and K. Goebel, Classical theory of nonexpansive mappings, in Handbook of Metric Fixed Point Theory, Kluwer, 49-91, 2001. MR1904274 (2004c:47105)
20. p-spaces, Journal of Functional Analysis 56 (1984), 29-78. MR735704 (86a:46085)
21. A.T. Lau and P.F. Mah, Normal structure in dual Banach spaces associated with a locally compact group, Trans. Amer. Math. Soc. 310 (1988), 341-353. MR937247 (89e:43004)
22. A.T. Lau and P.F. Mah, Quasi-normal structures for certain spaces of operators on a Hilbert space, Pacific Journal of Mathematics 121 (1986), 109-118. MR815037 (87f:47065)
23. A.T. Lau, P.F. Mah and A. Ulger, Fixed point property and normal structure for Banach spaces associated to locally compact groups,Proc.A.M.S.125 (1997), 2021-2027. MR1372037 (97i:43001)
24. A.T. Lau and A. Ulger, Some geometric properties on the Fourier and Fourier-Stieltjes algebras of locally compact groups, Arens regularity and related problems, Trans. Amer. Math. Soc. 337 (1993), 321-359. MR1147402 (93g:22007)
25. M. Leinert, On integration with respect to a trace, in Aspects of Positivity in Functional Analysis, North Holland Math. Stud. 122, 231-239, 1986. MR859732 (88b:46095)
26. M. Leinert, Integration und Ma/3, Vieweg 1995. MR1396785 (97j:28001)
27. 1 is uniformly Kadec-Klee, Proc. Amer. Math. Soc. 109 (1990), 71-77. MR943795 (90h:46029)
28. T.C. Lim, Asymptotic centres and nonexpansive mappings in conjugate spaces,Pacific J. Math. 90 (1980), 135-143. MR599326 (82h:47052)
29. 1, Seminaire d'Analyse Functionnelle 80-81, Ecole Polytechnique, Palaiseau, 1981. MR659309 (83h:47041)
30. P.S. Mostert, Sections in principal fibre spaces, Duke Math. J. 23 (1956), 57-71. MR0075575 (17:771f)
31. E. Nelson, Notes on non-commutative integration, Journal of Functional Analysis 15 (1974), 103-116. MR0355628 (50:8102)
32. T.W. Palmer, Classes of nonabelian, noncompact, locally compact groups,Rocky Mountain J. of Math. 8 (1978), 683-741. MR513952 (81j:22003)
33. M. Picardello, Lacunary sets in discrete noncommutative groups,Boll. Un.Math. Ital.(4) 8 (1973), 494-508. MR0344804 (49:9543)
34. I.E. Segal, Equivalences of measure spaces, Amer. J. Math. 73 (1951), 275-313. MR0041191 (12:809f)
35. M. Takesaki, Theory of Operator Algebras I, Springer-Verlag, New York, 1979. MR548728 (81e:46038)
36. K. Taylor, Geometry of the Fourier algebras and locally compact groups with atomic unitary representations, Math. Ann. 262 (1983), 183-190. MR690194 (84h:43020)
37. K. Yosida, Functional Analysis, Springer-Verlag, Berlin, Heidelberg, New York, 1978. MR0500055 (58:17765)