Skip to main content
SpringerLink
Log in

On bornologicalness in locally convex algebras

  • Original Article
  • Published:
Boletín de la Sociedad Matemática Mexicana Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allan, G.R.: A spectral theory for locally convex algebras. Proc. Lond. Math. Soc. (3) 15, 399–421 (1965)

    Article  MathSciNet  Google Scholar 

  2. Allan, G.R., Dales, H.G., McClure, J.P.: Pseudo-Banach algebras. Stud. Math. T.XL, 55–68 (1971)

    Article  MathSciNet  Google Scholar 

  3. Cochran, A.C.: Weak \(A\)-convex algebras. Proc. Am. Math. Soc. 26, 73–77 (1970)

    MathSciNet  MATH  Google Scholar 

  4. Cochran, A.C.: Representation of \(A\)-convex algebras. Proc. Am. Math. Soc. 41, 473–479 (1973)

    MathSciNet  MATH  Google Scholar 

  5. Cochran, A.C., Keown, R., Williams, C.R.: On a class of topological algebras. Pac. J. Math. 34, 17–25 (1970)

    Article  MathSciNet  Google Scholar 

  6. Haralampidou, M., Oudadess, M., Palacios, L., Signoret, C.: On different barrelledness notions in locally convex algebras. Bull. Belg. Math. Soc. Simon Stevin 22(1), 25–38 (2015)

    Article  MathSciNet  Google Scholar 

  7. Hogbé-Nlend, H.: Théorie des bornologies et applications. Lect Notes Mathematics, vol. 213. Springer, Berlin (1971)

    Book  Google Scholar 

  8. Horváth, J.: Topological Vector Spaces and Distributions. Addition-Wesley Publishing, Reading (1966)

    MATH  Google Scholar 

  9. Köthe, G.: Topological Vector Spaces I, Grundlehren Math Wiss Einz Band, vol. 159. Springer, New York (1969)

    Google Scholar 

  10. Mallios, A.: Topological algebras. Selected topics, North-Holland, Mathematics Studies 124, Amsterdam (1986)

  11. Michael, E.A.: Locally multiplicatively convex topological algebras. Mem. Am. Math. Soc. 11, 9 (1952)

  12. Oudadess, M.: Bounded structures in locally \(A\)-convex algebras, ICTAA 2008, 80–88, Math. Stud. (Tartu) 4, Est. Math. Soc., Tartu (2008)

  13. Oudadess, M.: Remarks on locally \(A\)-convex algebras. Bull. Greek Math. Soc. 56, 47–55 (2009)

    MathSciNet  MATH  Google Scholar 

  14. Oudadess, M.: Locally uniformly convex algebras (preprint; Ecole Normale Supérieure de Rabat, 2007)

  15. Oudadess, M.: Une norme d’algèbre de Banach dans les algèbres locallement uniformément A-convexes complètes. Afrika Math. IX, 15–22 (1987)

    MATH  Google Scholar 

  16. Oudadess, M.: Théoremes de type Gelfand–Naimark dans les algèbres uniformément A-convexes. Ann. Sci. Math. Québec 9(1), 73–82 (1985)

    MathSciNet  MATH  Google Scholar 

  17. Oudadess, M.: Subnormable A-convex algebras. In: Proceedings of the 8th International Conference on Topological Algebras and their Applications, 2014, in book Topological Algebras and their Applications, Berlin, Boston, De Gruyter, pp. 201–212 (2018)

  18. Schaëffer, H.H.: Topological Vector Spaces. Springer, New York (1971)

    Book  Google Scholar 

  19. Warner, S.: Inductive limits of normed algebras. Trans. Am. Math. Soc. 82, 190–216 (1956)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Athens Panepistimioupolis, 15784, Athens, Greece

    Marina Haralampidou

  2. École Normale Supérieure, Takadoum, BP 5118, 1000, Rabat, Morocco

    Mohamed Oudadess

  3. Universidad Autónoma Metropolitana Iztapalapa, 09340, Mexico City, Mexico

    Lourdes Palacios & Carlos Signoret

Authors
  1. Marina Haralampidou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Oudadess
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lourdes Palacios
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Carlos Signoret
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lourdes Palacios.

Additional information

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

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40590-020-00291-2

Keywords

Mathematics Subject Classification

Search

Navigation