Finite-dimensional right ideals in some algebras associated with a locally compact group

Filali, M.

doi:10.1090/S0002-9939-99-04631-6

Finite-dimensional right ideals in some algebras associated with a locally compact group
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Proc. Amer. Math. Soc. 127 (1999), 1729-1734 Request permission

Abstract:

Let $G$ be a discrete group, a commutative discrete cancellative semigroup or a locally compact abelian group. Let $UC(G)$ be the space of bounded, uniformly continuous, complex-valued functions on $G.$ With an Arens-type product, the conjugate $UC(G)^{*}$ becomes a Banach algebra. We prove, that unlike left ideals, finite-dimensional right ideals exist in $UC(G)^{*}$ if and only if $G$ is compact.

References

J. W. Baker and M. Filali, Minimal ideals in group algebras and their biduals, Math. Proc. Cambridge Philos. Soc. 120 (1996), 475–488.
John F. Berglund, Hugo D. Junghenn, and Paul Milnes, Analysis on semigroups, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1989. Function spaces, compactifications, representations; A Wiley-Interscience Publication. MR 999922
M. Filali, Right cancellation in $\beta S$ and $UG$, Semigroup Forum 52 (1996), no. 3, 381–388. MR 1377702, DOI 10.1007/BF02574113
M. Filali, The uniform compactification of a locally compact abelian group, Math. Proc. Cambridge Philos. Soc. 108 (1990), no. 3, 527–538. MR 1068454, DOI 10.1017/S0305004100069413
M. Filali, On the semigroup $\beta S$, Semigroup Forum (to appear).
Mahmoud Filali, Weak $p$-points and cancellation in $\beta S$, Papers on general topology and applications (Gorham, ME, 1995) Ann. New York Acad. Sci., vol. 806, New York Acad. Sci., New York, 1996, pp. 130–139. MR 1429649, DOI 10.1111/j.1749-6632.1996.tb49164.x
M. Filali, Finite-dimensional left ideals in some algebras associated with a locally compact group, Proc. Amer. Math. Soc. (to appear).
Edmond E. Granirer, The radical of $L^{\infty }(G)^{\ast }$, Proc. Amer. Math. Soc. 41 (1973), 321–324. MR 326302, DOI 10.1090/S0002-9939-1973-0326302-9
Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups. Integration theory, group representations, Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963. MR 0156915