Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T12:46:16.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Closed subalgebras of homogeneous Banach algebras

Published online by Cambridge University Press:  09 April 2009

Ching-Nan Tseng  and
Hawi-Chiuan Wang
Ching-Nan Tseng
Affiliation:
Institute of Mathematics National Tsing Hua UniversityTaiwan, Republic of China.
Hawi-Chiuan Wang
Affiliation:
Institute of Mathematics National Tsing Hua UniversityTaiwan, Republic of China.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Rudin's synthesis method for investigating closed subalgebras of L1(G), where G is an infinite compact abelian group, is extended to the study of closed subalgebras in homogeneous Banach algebras and Segal algebras. Necessary and sufficient conditions are given for the synthesis to hold in certain classes of homogeneous Banach algebras and it is proved that in the Ap(G) algebras the synthesis holds for 1 ≦ p 2 but fails for Ap(T), 2 < p < ∞.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 20 , Issue 3 , November 1975 , pp. 366 - 376
Copyright
Copyright © Australian Mathematical Society 1975

References

Edwards, R. E. (1967), Fourier series: a modern introduction, Vol. II (Holt, Rinehart and Winston, Inc., New York, 1967).Google Scholar
Hewitt, E. and Ross, K. A. (1970), Abstract harmonic analysis, Vol. II (Springer-Verlag, N. Y., Heidelberg, Berlin, 1970).Google Scholar
Kahane, J. P. (1965), ‘Idempotents and closed subalgebras of A(Z)’, Proc. Internat. Symp. On Function Algebras, Tulane Univ. 198–207.Google Scholar
Katznelson, Y. (1968), An introduction to harmonic analysis (John Wiley, New York, 1968).Google Scholar
Reiter, H. J. (1968), Classical harmonic analysis and locally compact group, Oxford Mathematical Monographs (Oxford University Press, Oxford, 1968).Google Scholar
Rider, D. (1969), ‘Closed sublagebras of L1(T)’, Duke Math. J. 36, 105–116.CrossRefGoogle Scholar
Rudin, W. (1962), Fourier analysis on groups (Interscience Publishers. New York, 1962).Google Scholar
Wang, H. C. (1972), ‘Nonfactorization in group algebras’, Siudia Math. 42, 231–241.Google Scholar