Abstract
We characterize the existence of the Bishop boundary in the context of an Urysohn (topological) algebra, by means ofG δ points. Considering a subset of its spectrum and the restriction of its Gel'fand transform algebra on the previous subset, we realize its Bishop boundary, as the trace of the Bishop boundary of the initial algebra on the spectrum of the restriction algebra. We get a generalization of the latter by considering a continuous algebra morphism.
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Bishop E.,A minimal boundary for function algebras. Pacific J. Math.9 (1959), 629–642.
Hadjigeorgiou R. I.,Spectral Geometry of Topological Algebras. Doctoral Thesis, Univ. of Athens, 1995.
Hadjigeorgiou R. I.,Bishop boundaries of topological tensor product algebras. Math. Japonica42 (1995), 471–487.
Hadjigeorgiou R. I.,Choquet boundaries in topological algebras Comment. Math.,36 (1996), 131–148.
Gillman L., Jerison M.,Rings of Continuous Functions. Springer-Verlag, New York, 1976.
Gulick S. L.,EThe minimal boundary ofE. Trans. Amer. Math. Soc.131 (1968), 303–314.
Mallios A.,Topological Algebras. Selected Topics. North-Holland, Amsterdam, 1986.
Mallios A.,The de Rham-Kähler complex of the Gel'fand sheaf of a topological algebra. J. Math. Anal. Appl.175 (1993), 143–168.
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This paper is based on and extends results of the author's Doctoral Thesis, written under the supervision of Professor A. Mallios (Univ. of Athens).
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Hadjigeorgiou, R.I. On the Bishop boundary in topological algebras. Rend. Circ. Mat. Palermo 46, 347–360 (1997). https://doi.org/10.1007/BF02844277
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DOI: https://doi.org/10.1007/BF02844277