Banach algebras with non-Hausdorff structure spaces

Banach algebras with non-Hausdorff structure spaces
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by Bertram Yood

Proc. Amer. Math. Soc. 123 (1995), 411-415

DOI: https://doi.org/10.1090/S0002-9939-1995-1216828-2

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An example due to G. W. Mackey is an instance of a class of Banach algebras whose spaces of primitive ideas are not Hausdorff spaces.

References

I. Gelfand and G. Šilov, Über verschiedene Methoden der Einführung der Topologie in die Menge der maximalen Ideale eines normierten Ringes, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 25–39 (German, with Russian summary). MR 0004729
C. W. Kohls, The space of prime ideals of a ring, Fund. Math. 45 (1957), 17–27. MR 100610, DOI 10.4064/fm-45-1-17-27
Nathan Jacobson, Structure of rings, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, 190 Hope Street, Providence, R.I., 1956. MR 0081264
Neal H. McCoy, The theory of rings, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0188241
Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
Bertram Yood, Structure spaces of rings and Banach algebras, Michigan Math. J. 31 (1984), no. 2, 181–189. MR 752254, DOI 10.1307/mmj/1029003022
Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029