Abstract
We investigate the problem whether every closed ideal in the group algebrasA(G) is generated by a single function. For the algebrasA r(R n),n≧6, we give a negative solution. We also obtain some negative results for general locally compact abelian groups.
Article PDF
Similar content being viewed by others
References
Y. Katznelson,An introduction to harmonic analysis, Wiley, 1968.
P. Malliavin,Impossibilité de la synthèse spectrale sur les groupes abéliens non compacts, Publ. Math. de Inst. Hautes Etudes Sci. Paris (1959), 61–68.
P. Malliavin,Calcul symbolic et sous-algèbres de L 1(G), Bull. Soc. Math. France,87 (1959), 181–190.
W. Rudin,Fourier analysis on groups, Interscience, 1962.
L. Schwartz,Sur une propriété de synthèse spectrale dans les groupes non compacts, C.R. Acad. Sci. Paris227 (1948), 424–426.
N. Th. Varopoulos,Spectral synthesis on spheres, Proc. Cambridge Phil. Soc.62 (1966), 379–387.
C. R. Warner,Closed ideals in the group algebra L 1(G) ∩L 2(G), Trans. Amer. Math. Soc.121 (1966), 408–423.
Author information
Authors and Affiliations
Additional information
This paper is a part of the author’s Ph. D. thesis prepared at the Hebrew University of Jerusalem under the supervision of Professor Y. Katznelson, to whom the author wishes to express his thanks for his helpful guidance, and valuable remarks.
Rights and permissions
About this article
Cite this article
Atzmon, A. Non-singly-generated closed ideals in group algebras. Israel J. Math. 7, 303–310 (1969). https://doi.org/10.1007/BF02788863
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02788863