On bornologicalness in locally convex algebras

Abstract

We give a synthetic presentation of several bornologicalness notions in locally convex algebras. Some of these notions are new. As in locally convex spaces, characterizations are given via (algebra) seminorms. A classification and examples are provided.

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Acknowledgements

We would like to thank the referees for their useful comments and remarks.

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Correspondence to Lourdes Palacios.

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To the memory of our good friend and coauthor Mohamed Oudadess.

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Haralampidou, M., Oudadess, M., Palacios, L. et al. On bornologicalness in locally convex algebras. Bol. Soc. Mat. Mex. 26, 1183–1194 (2020). https://doi.org/10.1007/s40590-020-00291-2

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Keywords

  • Bornology
  • Bornological space
  • i-Bornological algebra

Mathematics Subject Classification

  • Primary 46H05
  • 46H20
  • Secondary 46J10