Weak spectral synthesis in commutative Banach algebras

Journal of Functional Analysis

Volumn 254, Issue 4, 2008, Pages 987-1002

  Kaniuth, Eberhard ^a  

^a UNIVERSITY OF PADERBORN   (Germany)

Author keywords

Commutative Banach algebra; Ditkin Shilov theorem; Fourier algebra; Injection theorem; Projective tensor product; Structure space; Weak Ditkin set; Weak spectral set

Indexed keywords

EID: 38049092036     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2007.10.002     Document Type: Article

References (21)

1. Atzmon A. Spectral synthesis in regular Banach algebras. Israel J. Math. 8 (1970) 197-212
2. Atzmon A. On the union of sets of synthesis and Ditkin's condition in regular Banach algebras. Bull. Amer. Math. Soc. 2 (1980) 317-320
3. Badé W., and Curtis Jr. P.C. The Wedderburn decomposition of commutative Banach algebras. Amer. J. Math. 82 (1960) 851-866
4. Benedetto J.J. Spectral Synthesis (1975), Teubner, Stuttgart
5. Dales H.G. Banach Algebras and Automatic Continuity. London Math. Soc. Monogr. (2000), Clarendon, Oxford
6. Eymard P. L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92 (1964) 181-236
7. Kaniuth E. Weak spectral synthesis for the projective tensor product of commutative Banach algebras. Proc. Amer. Math. Soc. 132 (2004) 2959-2967
8. Kaniuth E., and Lau A.T. Spectral synthesis for A (G) and subspaces of VN (G). Proc. Amer. Math. Soc. 129 (2001) 3253-3263
9. Malliavin P. Impossibilitè de la synthèse spectrale sur les groupes abéliens non compacts. Inst. Hautes Études Sci. Publ. Math. 2 (1959) 61-68
10. Mirkil H. A counterexample to discrete spectral synthesis. Compos. Math. 14 (1960) 269-273
11. Muraleedharan M., and Parthasarathy K. Difference spectrum and spectral synthesis. Tohoku Math. J. 51 (1999) 65-73
12. Parthasarathy K., and Varma S. On weak spectral synthesis. Bull. Austral. Math. Soc. 43 (1991) 279-282
13. Reiter H., and Stegeman J.D. Classical Harmonic Analysis and Locally Compact Groups (2000), Oxford Univ. Press
14. Rudin W. Fourier Analysis on Groups (1962), Interscience, New York
15. Sherbert D.R. The structure of ideals and point derivations in Banach algebras of Lipschitz functions. Trans. Amer. Math. Soc. 111 (1964) 240-272
16. Takesaki M., and Tatsuuma N. Duality and subgroups. II. J. Funct. Anal. 11 (1972) 184-190
17. Varopoulos N.Th. Spectral synthesis on spheres. Proc. Cambridge Philos. Soc. 62 (1966) 379-387
18. Varopoulos N.Th. Tensor algebras and harmonic analysis. Acta Math. 119 (1968) 51-112
19. Warner C.R. Weak spectral synthesis. Proc. Amer. Math. Soc. 99 (1987) 244-248
20. Warner C.R. Spectral synthesis in the Mirkil algebra. J. Math. Anal. Appl. 167 (1992) 176-182
21. Zelmanov E.I. On periodic compact groups. Israel J. Math. 77 (1992) 83-95