Can an $\textrm {LCA}$ group be anti-self-dual?
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- by D. L. Armacost
- Proc. Amer. Math. Soc. 27 (1971), 186-188
- DOI: https://doi.org/10.1090/S0002-9939-1971-0267036-7
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Abstract:
We say that a topological group $G$ is anti-self-dual if there are no nontrivial continuous homomorphisms from $G$ into the character group $\hat G$ or from $\hat G$ into $G$. We show that no nontrivial LCA group can be anti-self-dual.References
- Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin-New York, 1979. Structure of topological groups, integration theory, group representations. MR 551496, DOI 10.1007/978-1-4419-8638-2
- Lewis C. Robertson, Connectivity, divisibility, and torsion, Trans. Amer. Math. Soc. 128 (1967), 482β505. MR 217211, DOI 10.1090/S0002-9947-1967-0217211-6 β, Transfinite torsion, $p$-constituents, and splitting in locally compact abelian groups, Mimeographed Notes, University of Washington, Seattle, Wash.
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 186-188
- MSC: Primary 22.20
- DOI: https://doi.org/10.1090/S0002-9939-1971-0267036-7
- MathSciNet review: 0267036