Hostname: page-component-7bb8b95d7b-nptnm Total loading time: 0 Render date: 2024-09-06T23:21:56.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Norms and spectra for certain subalgebras of M(G)

Published online by Cambridge University Press:  24 October 2008

C. Karanikas  and
J. H. Williamson
C. Karanikas
Affiliation:
University of Crete, Iraklion
J. H. Williamson
Affiliation:
Heriot-Watt University, Edinburgh
Get access Rights & Permissions [Opens in a new window]

Extract

We are concerned in this paper with the same general problem as in [4], that is, the relation between the spectral and norm properties of a sub-algebra of M(G) and the corresponding properties of the algebra of its ‘transforms’ in some sense. The spirit of the investigation is akin to that of the earlier paper, and some of the results obtained here directly generalize those of [4]. There are, however, considerable differences in scope and method.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 109 - 122
Copyright
Copyright © Cambridge Philosophical Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Boas, R. P.. Entire Functions (Academic Press, 1954).Google Scholar
[2] Dixmier, J.. C *-algebras (North-Holland, 1977).Google Scholar
[3] Fell, J. M. G.. Weak containment and induced representations of groups. Canad. J. Math. 14 (1962), 237–268.CrossRefGoogle Scholar
[4] Fountain, J. B., Ramsay, R. W. and Williamson, J. H.. Functions of measures on compact groups. Proc. Roy. Irish Acad. Sect. A 76 (1976), 235–251.Google Scholar
[5] Greenleaf, F. P.. Invariant Means on Topological Groups (Van Nostrand, 1969).Google Scholar
[6] Herz, C. S.. The theory of p-spaces with an application to convolution operators. Trans. Amer. Math. Soc. 154 (1971), 69–82.Google Scholar
[7] Herz, C. S.. Une généralisation de la notion de transformée de Fourier-Stieltjes. Ann. Inst. Fourier (Grenoble) 24 (1974), 145–157.CrossRefGoogle Scholar
[8] Hewitt, E. and Ross, K.. Abstract Harmonic Analysis, vols. I, II (Springer-Verlag, 1963, 1970).Google Scholar
[9] Katznelson, Y. and McGehee, C.. Some Banach algebras associated with quotients of L 1(R). Indiana Univ. Math. J. 21 no. 5 (1971), 419–436.CrossRefGoogle Scholar
[10] Naimark, M. A.. Normed Algebras, rev. ed. (Noordhoff, 1972).Google Scholar
[11] Palmer, T. W.. Classes of nonabelian, noncompact, locally compact groups. Rocky Mountain J. Math. 8 (1978), 683–741.CrossRefGoogle Scholar
[12] Pedersen, G. K.. C*-algebras and their Automorphism Groups (Academic Press, 1979).Google Scholar
[13] Wang, P. S.. On isolated points in the dual spaces of locally compact groups. Math. Ann. 218 (1975), 19–34.CrossRefGoogle Scholar
[14] Wichmann, J.. The symmetric radical of an algebra with involution. Arch. Math. (Basel) 30 (1978), 83–88.CrossRefGoogle Scholar