A Separation Property of Positive Definite Functions on Locally Compact Groups and Applications to Fourier Algebras

Journal of Functional Analysis

Volumn 175, Issue 1, 2000, Pages 89-110

  Kaniuth, Eberhard ^a   Lau, Anthony T ^b  

^a UNIVERSITY OF PADERBORN   (Germany)

^b UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037911681     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3612     Document Type: Article

References (28)

1. Bernat P. Représentations des groupes de Lie résolubles. 1972;Dunod, Paris.
2. Chou C. Almost periodic operators on VN(G). Trans. Amer. Math. Soc. 317:1990;229-253.
3. Cowling M., Rodway P. Restrictions of certain function spaces to closed subgroups of locally compact groups. Pacific J. Math. 80:1979;91-104.
4. p(G). Proc. Amer. Math. Soc. 124:1996;1159-1169.
5. Derighetti A. Quelques observations concernant les ensembles de Ditkin d'un groupe localement compact. Monatsh. Math. 101:1986;95-113.
6. Derighetti A. Convoluteurs et projecteurs. Harmonic Analysis. Lecture Notes in Math. 1359:1988;Springer-Verlag, New York/Berlin. p. 142-158.
7. Dixmier J. C*-Algebras. 1977;North-Holland, Amsterdam.
8. Dunford N., Schwartz J. T. Linear Operators, I. 1957;Interscience, New York.
9. Eymard P. L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France. 92:1964;181-236.
10. Forrest B. Amenability and bounded approximate identities in ideals of A(G). Illinois J. Math. 34:1990;1-25.
11. Forrest B. Amenability and ideals in A(G). J. Austral. Math. Soc. Ser. A. 53:1992;143-155.
12. Granirer E. E. Weakly almost periodic and uniformly continuous functionals on the Fourier algebra of any locally compact group. Trans. Amer. Math. Soc. 189:1974;372-382.
13. Grosser S., Moskowitz M. Compactness conditions in topological groups. J. Reine Angew. Math. 246:1971;1-40.
14. Henrichs R. W. Fortsetzung positiv definiter Funktionen. Math. Ann. 232:1978;131-150.
15. Hewitt E., Ross K. A. Abstract Harmonic Analysis, II. 1970;Springer-Verlag, Berlin/Heidelberg/New York.
16. Hofmann K. H., Mostert P. Splitting in topological groups. Mem. Amer. Math. Soc. 43:1963.
17. E. Kaniuth, and, A. T. Lau, Spectral synthesis for A(G) and subspaces of VN(G), Proc. Amer. Math. Soc, to appear.
18. Lau A. T. Uniformly continuous functionals on the Fourier algebra of any locally compact group. Trans. Amer. Math. Soc. 251:1979;39-59.
19. ∞(G) and amenable locally compact groups. Pacific J. Math. 123:1986;149-159.
20. Leptin H. Sur l'algèbre de Fourier d'un groupe localement compact. C.R. Acad. Sci. Paris Sér. A. 266:1968;1180-1182.
21. Liukkonen J. R., Mislove M. W. Symmetry in Fourier-Stieltjes algebras. Math. Ann. 217:1975;97-112.
22. McMullen J. R. Extensions of positive definite functions. Mem. Amer. Math. Soc. 117:1972.
23. Montgomery D., Zippin L. Topological Transformation Groups. 1955;Interscience, New York.
24. Palmer T. W. Banach Algebras and the General Theory of*-algebras, I. 1994;Cambridge University Press, Cambridge.
25. Poncet J. Une classe d'espaces homogènes possédant une mesure invariante. C.R. Acad. Sci. Paris. 238:1954;553-554.
26. Roelcke W., Dierolf S. Uniform Structures on Topological Groups and Their Quotients. 1981;McGraw-Hill, New York.
27. Takesaki M., Tatsuuma N. Duality and subgroups, II. J. Funct. Anal. 11:1972;184-190.
28. Warner G. Harmonic Analysis on Semi-simple Lie Groups, I. 1972;Springer-Verlag, Berlin/Heidelberg/New York.