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On TQ-Algebras

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Abstract

A topological algebra A is called a Q-algebra if its set of quasi-invertible elements (of invertible elements, if A is unital) is an open set. This class of topological algebras has been extensively studied by several authors, but mostly in unital or commutative case. Properties of (not necessarily unital or commutative) TQ-algebras and, in the special case, of TQ-algebras with functional topological spectrum are given in the present paper.

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References

  1. Abel, M.: Advertive topological algebras. General topological algebras (Tartu, 1999). Math. Stud. (Tartu) 1, 14–24 (2001)

    MathSciNet  MATH  Google Scholar 

  2. Abel, M.: Inductive limits of Gelfand–Mazur algebras. Int. J. Pure. Appl. Math. 16(3), 363–378 (2004)

    MathSciNet  MATH  Google Scholar 

  3. Abel, M., Żelazko, W.: Properties of \(TQ\)-algebras. Proc. Est. Acad. Sci. 60(3), 141–148 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Arizmendi, H., Carrillo, A., Palacios, L.: On \(Q_{t}\)-algebras. Topological algebras and applications. Contemp. Math. 427, 49–55 (2007)

    Article  MATH  Google Scholar 

  5. Choukri, R., El Kinani, A.: Topological algebras whit ascending or descending chain condition. Arch. Math. (Basel) 72, 438–443 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fragoulopoulou, M.: Topological Algebras with Involution. North-Holland Mathematics Studies, vol. 200. Elsevier Science B.V., Amsterdam (2005)

    MATH  Google Scholar 

  7. Kaplansky, I.: Topological rings. Bull. Am. Math. Soc. 54(9), 809–826 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hadjigeorgiou, R.: On some more characterizations of Q-algebras. Topological algebras and their applications. Contemp. Math. 341, 49–61 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Hadjigeorgiou, R.: Topologically Q-algebras, more. Bull. Belg. Math. Soc. Simon Stevin 18(4), 695–706 (2011)

    MathSciNet  MATH  Google Scholar 

  10. Horváth, J.: Topological Vector Spaces and Distributions, vol. I. Addison Wesley Publ. Co., Reading (1966)

    MATH  Google Scholar 

  11. Mallios, A.: Topological Algebras. Selected Topics. North-Holland Mathematics Studies, vol. 124. Noth-Holland Public. Co., Amsterdam (1986)

    MATH  Google Scholar 

  12. Najmi, A.: Topologically Q-algebras. Bull. Greek Math. Soc. 52, 133–142 (2006)

    MathSciNet  MATH  Google Scholar 

  13. Schaefer, H., Wolff, M.: Topological Vector Spaces. Graduate Texts in Mathematics, vol. 3, 2nd edn. Springer, New York (1999)

    Book  Google Scholar 

  14. Semadeni, Z.: Banach spaces of continuous functions. In: Monografie Matematyczne, Tom 55, vol. I. PWN—Polish Scientific Publishers, Warsaw (1971)

  15. Tsertos, Y.: A characterization of \(Q\)-Algebras. Funct. Anal. Approx. Theory Numer. Anal. 11, 277–280 (1994)

    MathSciNet  MATH  Google Scholar 

  16. Waelbroeck, L.: Topological Vector Spaces and Algebras. Lecture Notes in Mathematics, vol. 230. Springer, Berlin (1973)

    Google Scholar 

  17. Warner, S.: Polynomial completeness in locally multiplicatively convex algebras. Duke Math. 23, 1–11 (1956)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Research of the first author is in part supported by the Institutional Research Funding IUT20–57 of the Estonian Ministry of Education and Research. The third author is supported by a Scholarship of CONACyT Mexico. We are greatly indebted to the referee for careful reading of the paper and for valuable remarks.

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Authors and Affiliations

  1. Institute of Pure Mathematics, University of Tartu, 46 Vanemuise Str. 232, 51014, Tartu, Estonia

    Mati Abel

  2. Departamento de Matemáticas, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Avenida San Rafael Atlixco, #186, Apartado Postal 55-532, 09340, México, D.F., Mexico

    Lourdes Palacios & Yuliana de Jesús Zárate-Rodríguez

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  1. Mati Abel
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  2. Lourdes Palacios
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  3. Yuliana de Jesús Zárate-Rodríguez
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Correspondence to Lourdes Palacios.

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Abel, M., Palacios, L. & Zárate-Rodríguez, Y.d.J. On TQ-Algebras. Mediterr. J. Math. 14, 184 (2017). https://doi.org/10.1007/s00009-017-0983-x

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  • DOI: https://doi.org/10.1007/s00009-017-0983-x

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