Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-20T06:56:58.215Z Has data issue: false hasContentIssue false
  • English
  • Français

Derivations on a Fréchet convolution algebra associated with a weight

Published online by Cambridge University Press:  24 October 2008

J. P. McClure
J. P. McClure
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Canada, R3T 2N2
Get access Rights & Permissions [Opens in a new window]

Abstract

For certain Fréchet convolution algebras associated with a weight w on the half-line [0, ∞), we are interested in the question of which Radon measures on [0, ∞) determine the derivations on the algebra. For particular weights, we show that the derivations are determined by those measures in the multiplier algebra of the original algebra. However, we also give an example of a weight for which that characterization fails. The results show a connection between the space of derivations and the behaviour for large y of the ratio w(x + y)/w(x) w(y).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 1 , July 1992 , pp. 175 - 181
Copyright
Copyright © Cambridge Philosophical Society 1992

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]Ghahramani, F.. Homomorphisms and derivations on weighted convolution algebras. J. London Math. Soc. (2) 21 (1980), 144–161.Google Scholar
[2]Ghahkamani, F.. The group of automorphisms of L l(0,1) is connected. Trans. Anier. Math. Soc. 314 (1989), 851–859.Google Scholar
[3]Ghahramani, F. and McClure, J. P.. Automorphisms of radical weighted convolution algebras. J. London Math. Soc. (2) 41 (1990), 122–132.CrossRefGoogle Scholar
[4]Ghahramani, F. and McClure, J. P.. Automorphisms and derivations on a Fréchet algebra of locally integrable functions. Preprint.Google Scholar
[5]Jewell, N. P. and Sinclair, A. M.. Epimorphisms and derivations on L 1(Q, 1) are continuous. Bull. London Math. Soc. 8 (1976), 135–139.CrossRefGoogle Scholar
[6]Kamowitz, H. and Scheinberg, S.. Derivations and automorphisms of L 1(0,1). Trans. Anier. Math. Soc. 135 (1969), 415–427.Google Scholar
[7]McClure, J. P.. Derivations of convolution algebras. Proc. Centre Math. Anal. Austral. Nat. Univ. 21 (1989), 318–327.Google Scholar
[8]Michael, E. A.. Locally Multiplicatively-convex Topological Algebras. Memoirs Amer. Math. Soc. no. 11 (American Mathematical Society, 1952).CrossRefGoogle Scholar
[9]Olver, F. W. J.. Asymptotics and Special Functions (Academic Press, 1974).Google Scholar