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On certain open problems in topological algebras

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Presentiamo qui alcuni problemi aperti sulle algebre topologiche. Questo articolo è una versione leggermente modificata di [25] (un articolo scritto in polacco che dovrebbe apparire negli Atti di un congresso locale tenuto a Szczin nell'autunno 1988). Abbiamo aggiunto qui una proposizione che afferma che ogni algebra reale o complessa può essere topologizzata in modo da renderla un'algebra semi-topologica localmente convessa, e abbiamo fatto molte piccole modifiche.

Gran parte dei problemi riportati qui o in [25] sono pubblicati per la prima volta.

Summary

We present here a number of open problems concerning topological algebras. This is a slightly modified version of [25] (a paper written in Polsh and supposed to be edited in the Proceedings of a local conference held in Szczecin in fall 1988). We added here a proposition stating that every real or complex algebra can be so topologized that it becomes a locally convex semi-topological algebra, and made several small changes. Most of the problems stated here or in [25] are published for the first time.

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References

  1. Arens R.,The space Lω and convex topological rings. Bull. Amer. Math. Soc. 52 (1946), 931–935.

    Article  MATH  MathSciNet  Google Scholar 

  2. Arens A.,Linear topological division algebras. Ibidem 53 (1947), 623–630.

    Article  MATH  MathSciNet  Google Scholar 

  3. Arens R.,Dense inverse limit rings. Michigan Math. J. 5 (1958), 169–182.

    Article  MATH  MathSciNet  Google Scholar 

  4. Atzmon A.,An operator without invariant subspaces on a nuclear Fréchet space. Ann. of Math. (2) 117 (1983), No. 3, 669–694.

    Article  MathSciNet  Google Scholar 

  5. Banach S.,Remarques sur les corps et groupes metriques. Studia Math. 10 (1948), 178–181.

    MATH  MathSciNet  Google Scholar 

  6. Beauzamy B.,Un operateur sans sous-espace invariant: simplification de l'example de P. Enflo. Integral Eq. Operator Theory 8 (1985), 314–384.

    Article  MATH  MathSciNet  Google Scholar 

  7. Behncke H.,Problem No 9. Banach Centre Publ. 8 (1982) p. 599.

    MathSciNet  Google Scholar 

  8. Enflo P.,On the invariant subspace problem for Banach spaces. Acta Math. 158 (1987) No. 3-4, 213–313.

    Article  MATH  MathSciNet  Google Scholar 

  9. Husain T.,Multiplicative functionals on topological algebras. Pitman Adv. Publ. Progr., Research Notes in Math. No 85, 1983.

  10. Michael E.,Locally multiplicatively-convex topological algebras. Mem. Amer. Math. Soc. 11, 1952.

  11. Mityagin B., Rolewicz S., Żelazko W.,Entire functions in B c -algebras. Studia Math. 21 (1962), 291–306.

    MathSciNet  Google Scholar 

  12. Read C. J.,A solution to the invariant subspace problem. Bull. London Math. Soc. (2) 16 (1984), 337–401.

    Article  MATH  MathSciNet  Google Scholar 

  13. Read C. J.,A solution to the invariant subspace problem for the space l 1. Ibidem 17 (1985), 305–317.

    Article  MATH  MathSciNet  Google Scholar 

  14. Read C. J.,A short proof concerning the invariant subspace problem. J. London Math. Soc. (2) 34 (1986), 335–348.

    Article  MATH  MathSciNet  Google Scholar 

  15. Rolewicz S.,Metric Linear Spaces. Monografie Mat. 56, Warszawa 1972.

  16. Turpin Ph.,Un remarque sur les algèbres à inverse continu. C. R. Acad. SC. Paris 270. A1686–A1689.

  17. Waelbroeck L.,Topological vector spaces and algebras. Lect. Not. Math. 230, Springer Verlag 1971.

  18. Żelazko W.,A theorem on B 0-division algebras. Bull. Polon. Acad. Sc. 8, (1960), 373–375.

    Google Scholar 

  19. Żelazko W.,Metric genralizations of Banach algebras. Rozprawy Mat. (Dissertationes Math.) 47, 1965.

  20. Żelazko W.,Banach algebras. Amsterdam 1973.

  21. Żelazko W.,Selected topics in topological algebras. Aarhus Univ. Lecture Notes No 31, 1971.

  22. Żelazko W.,On maximal ideals in commutative m-convex algebras. Studia Math. 58 (1976), 291–298.

    MathSciNet  Google Scholar 

  23. Żelazko W.,Functional continuity of commutative m-convex B 0-algebras with countable maximal ideal spaces. Coll. Math. 51 (1987), 395–399.

    Google Scholar 

  24. Żelazko W.,A non-m-convex algebra on which operate all entire functions. Ann. Polon. Math. 46 (1985), 389–394.

    MathSciNet  Google Scholar 

  25. Żelazko W.,O pewnych otwartych problemach teorii algebr topologicznych. Proc. Conf. Szczecin 1988 (in print).

  26. Żelazko W.,Example of an algebra which is non-topologizable as a locally convex topological algebra.

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  1. W. Żelazko
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dell'Instituto di Matematica, Academia Polacca delle Scienze

(Conferenza tenuta il 20 marzo 1989)

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Żelazko, W. On certain open problems in topological algebras. Seminario Mat. e. Fis. di Milano 59, 49–58 (1989). https://doi.org/10.1007/BF02925291

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