Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-29T19:12:31.782Z Has data issue: false hasContentIssue false
  • English
  • Français

Multipliers of certain convolution algebras over locally compact semigroups

Published online by Cambridge University Press:  24 October 2008

D. G. Todd
D. G. Todd
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we extend a result of Johnson and Lahr(3), which characterizes the multiplier algebra of L1(a, b) (the algebra of Lebesgue integrable functions on the interval of real numbers from a to b, under order convolution) to the L1 algebra of a general totally ordered semigroup. Similar work has been done in (l), but under more restrictive conditions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 87 , Issue 1 , January 1980 , pp. 51 - 59
Copyright
Copyright © Cambridge Philosophical Society 1980

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)Akinyele, O.A multiplier problem for a semigroup algebra of an ordered semigroup. Le Matematiche 30, fasc. 1 (1975), 133–150.Google Scholar
(2)Dunford, M. & Schwartz, J. T.Linear Operators. 1. General Theory (Interscience Publishers, 1958).Google Scholar
(3)Johnson, D. L. & Lahr, C. D.Multipliers of L 1 algebras with order convolution. Notices Amer. Math. Soc. 24 (1977), A 566.Google Scholar
(4)Lahr, C. D.Multipliers for certain convolution measure algebras. Trans. Amer. Math. Soc. 185 (1973), 165–181.Google Scholar
(5)Pym, J. S.The convolution of linear functionals. Proc. London Math. Soc. (3) 14 (1964), 431–444.CrossRefGoogle Scholar
(6)Rigelhof, R.Invariant measures on locally compact semigroups. Proc. Amer. Math. Soc. 28 (1971), 173–176.CrossRefGoogle Scholar
(7)Rothman, N. J.An L 1 algebra for certain locally compact topological semigroups. Pacific J. Math. 23 (1967), 143–151.Google Scholar
(8)Schaefer, H. H.Banach lattices and positive operators (Springer-Verlag, 1974).CrossRefGoogle Scholar
(9)Wendel, J. G.On isometric isomorphism of group algebras. Pacific J. Math. 1 (1951), 305–311.CrossRefGoogle Scholar
(10)Wendel, J. G.Left centralizers and isomorphisms of group algebras. Pacific J. Math. 2 (1952), 251–261.CrossRefGoogle Scholar
(11)Yuan, J.On the convolution algebra of H-invariant measures. Pacific J. Math. 62 (1976), 595–600.CrossRefGoogle Scholar