Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-17T01:09:02.417Z Has data issue: false hasContentIssue false

A characterization of quotient algebras of Ll(G)

Published online by Cambridge University Press:  24 October 2008

Donald E. Ramirez
Affiliation:
University of Virginia

Extract

Let G be a locally compact Abelian group; Γ the dual group of G; C0(Γ) the algebra of continuous functions on Γ which vanish at infinity; CB(Γ) the continuous, bounded functions on Γ; M (G) the algebra of bounded Borel measures on G; L1(G) the algebra of absolutely continuous measures; and M(G)∩ the algebra of Fourier–Stieltjes transforms.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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)Buck, R. C.Bounded continuous functions on a locally compact space. Michigan Math. J. 5 (1958), 95104.CrossRefGoogle Scholar
(2)Dunford, N. and Schwartz, J.Linear Operators Part I. (Interscience Publishers; New York, 1958).Google Scholar
(3)Katznelson, Y. and McGehee, C. Measures and pseudomeasures on compact subsets of the line (to appear).Google Scholar
(4)Schaefer, H.Topological vector spaces. (Macmillan; New York, 1966).Google Scholar
(5)Ramirez, D.Uniform approximation by Fourier-Stieltjes Transforms. Proc. Cambridge Philos. Soc. 64 (1968), 323333.CrossRefGoogle Scholar
(6)Rudin, W.Fourier Analysis on Groups. (Interscience Publishers; New York, 1962).Google Scholar
(7)Rosenthal, H.A characterization of restrictions of Fourier-Stieltjes transforms. Pacific J. Math. 23 (1967), 403418.CrossRefGoogle Scholar
(8)Vabopoulos, N.On a problem of a A. Beurling. J. functional analysis 2 (1968), 2430.CrossRefGoogle Scholar
(9)Edwards, R. B.Uniform approximation on noncompact spaces. Trans. Amer. Math. Soc. 122 (1966), 249276.CrossRefGoogle Scholar
(10)Kaufman, R.Transforms of Certain Measures. Michigan Math. J. 14 (1967), 449452.CrossRefGoogle Scholar