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Commutative lmc algebras with discrete spectrum

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Abstract

SupposeE is a topological algebra with non-empty spectrum Gel'fand spaceM(E) andE M(E)) the algebra of allC-valued continuous functions onM(E). EndowE M(E) with the topologies “c”, “e” of compact resp. equicontinuous convergence. ThenE M (E) characterizes all unital (commutative) semisimple complete lmc algebras with discrete spectrum, while all unital uniform complete lmc algebras with dispersed spectrum are of the formE(E)). The first result may fail if completeness is dropped. The second one fails if “e” is replaced by “c” even ifE is complete.

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Authors and Affiliations

  1. Bahnhofstrasse 13, D-91257, Pegnitz, Germany

    Helmut Goldmann & Maria Fragoulopoulou

  2. Department of Mathematics, University of Athens, Panepistemiopolis, 157 84, Athens, Greece

    Helmut Goldmann & Maria Fragoulopoulou

Authors
  1. Helmut Goldmann
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  2. Maria Fragoulopoulou
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Additional information

The part of the work due to the 2nd author was carried out during her 3-month visit at the Institute of Mathematics, Univ. of Münster (Germany) in Spring of 1995. The warm hospitality from Professor Dr. G. Maltese and the financial support from a DAAD grant are thankfully acknowledged.

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Goldmann, H., Fragoulopoulou, M. Commutative lmc algebras with discrete spectrum. Rend. Circ. Mat. Palermo 46, 371–389 (1997). https://doi.org/10.1007/BF02844279

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  • DOI: https://doi.org/10.1007/BF02844279

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