A Theorem on Algebras of Measures on Topological Groups

J. H. Williamson

doi:10.1017/S0013091500021908

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Let G be a locally compact Abelian group, and the set of bounded complex (regular countably-additive Borel) measures on G. It is well known that becomes a Banach space if the norm is defined by

the supremum being over all finite sets of disjoint Borel subsets of G.

References

REFERENCES

Hewitt, E., The asymmetry of certain algebras of Fourier-Stieltjes transforms,Michigan Math. J., 5 (1958), 149–158.CrossRef Google Scholar

šreder, Yu. A., The structure of maximal ideals in rings of measures with convolution, Mat. Sbornik N.S., 27 (69) (1950), 297–318; American Mathematical Society Translation no. 81.Google Scholar

Wiener, N. and Pitt, H. R., On absolutely convergent Fourier-Stieltjes transforms, Duke Math. J., 4 (1938), 420–436.CrossRef Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Williamson, J. H. 1962. The Wiener-Pitt Phenomenon on the Half-Line. Proceedings of the Edinburgh Mathematical Society, Vol. 13, Issue. 1, p. 37.

Davis, T. A. 1963. The Wiener–Pitt phenomenon on semi-groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 59, Issue. 1, p. 11.

Johnson, B. E. 1964. Isometric isomorphisms of measure algebras. Proceedings of the American Mathematical Society, Vol. 15, Issue. 2, p. 186.

Varopoulos, N. Th. 1965. A note on the abstract Wiener-Pitt phenomenon. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 61, Issue. 1, p. 297.

Johnson, B. E. 1967. Continuity of linear operators commuting with continuous linear operators. Transactions of the American Mathematical Society, Vol. 128, Issue. 1, p. 88.

Johnson, B. E. 1967. Symmetric maximal ideals in 𝑀(𝐺). Proceedings of the American Mathematical Society, Vol. 18, Issue. 6, p. 1040.

Drury, S. W. 1968. Properties of certain measures on a topological group. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 64, Issue. 4, p. 1011.

Johnson, B. E. 1968. The Šilov boundary of 𝑀(𝐺). Transactions of the American Mathematical Society, Vol. 134, Issue. 2, p. 289.

Taylor, Joseph L. 1971. The cohomology of the spectrum of a measure algebra. Acta Mathematica, Vol. 126, Issue. 0, p. 195.

Zafran, Misha 1982. Harmonic Analysis. Vol. 908, Issue. , p. 228.

Brown, G. Karanikas, C. and Williamson, J. H. 1982. The asymmetry of M0(G). Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 91, Issue. 3, p. 407.

Kakutani, Shizuo Anzai, Hirotada Kodaira, Kunihiko and Hewitt, Edwin 1986. Shizuo Kakutani. p. 59.

1988. Banach *-Algebraic Bundles, Induced Representations, and the Generalized Mackey Analysis. Vol. 126, Issue. , p. 1373.

1988. Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles: Basic Representation Theory of Groups and Algebras. Vol. 125, Issue. , p. 643.

1990. Fourier Analysis on Groups. p. 271.

Hatori, Osamu 1998. Measures with natural spectra on locally compact abelian groups. Proceedings of the American Mathematical Society, Vol. 126, Issue. 8, p. 2351.

Bisbas, Antonis 1999. Singular measures with absolutely continuous convolution squares on locally compact groups. Proceedings of the American Mathematical Society, Vol. 127, Issue. 10, p. 2865.

Ohrysko, Przemysław Wojciechowski, Michał and Graham, Colin C. 2016. Non-separability of the Gelfand space of measure algebras. Arkiv för Matematik, Vol. 54, Issue. 2, p. 525.

Ohrysko, Przemysław and Wasilewski, Mateusz 2019. Spectral theory of Fourier–Stieltjes algebras. Journal of Mathematical Analysis and Applications, Vol. 473, Issue. 1, p. 174.

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A Theorem on Algebras of Measures on Topological Groups

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