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On weak and Schauder ℱ-bases in topological vector spaces

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References

  1. N.Adasch, B.Ernst and D.Keim, Topological vector spaces. LNM639, Berlin-Heidelberg-New York 1978.

  2. M.Bilbao, Espacios de sucesiones y sumabilidad Abel. Tesis Doctoral, Sevilla 1982.

  3. T.Casasús, Algunos nuevos resultados en gráfica cerrada. Tesis Doctoral, Valencia 1986.

  4. M. de Wilde, On weak and Schauder decompositions. Studia Math.61, 145–148 (1972).

    Google Scholar 

  5. M.de Wilde, Closed graph theorems and webbed spaces. Research Notes in Math.19, London 1978.

  6. M. de Wilde andC. Houet, On increasing sequences of absolutely convex sets in locally convex spaces. Math. Ann.192, 257–261 (1971).

    Google Scholar 

  7. M. Florencio andP. Pérez, Sobre sumabilidad Césaro en el espacio CS (I). Rev. Real Ac. Ciencias Madrid75, 1185–1197 (1981).

    Google Scholar 

  8. M.García, Sobre ciertos tipos de sumabilidades: dualidad y bases. Tesis Doctoral, Valencia 1982.

  9. B. R. Gelbaum, Expansions in Banach spaces. Duke Math. J.17, 187–196 (1950).

    Google Scholar 

  10. T.Husain and S. M.Khaleelulla, Barrelledness in topological and ordered vector spaces. LNM692, Berlin-Heidelberg-New York 1978.

  11. A. Jakimowski, W. Meyer-König andK. Zeller, Power series methods of summability: positivity and gap perfectness. Trans. Amer. Math. Soc.266, 309–317 (1981).

    Google Scholar 

  12. H.Jarchow, Locally convex spaces. Stuttgart 1981.

  13. N. J. Kalton, Basic sequences inF-spaces and their applications. Proc. Edinburgh Math. Soc.19, 151–167 (1974).

    Google Scholar 

  14. V. Ya. Kozlov, On a generalization of the notion of basis. Dokl. Akad. Nauk. SSSR73, 643–646 (1950).

    Google Scholar 

  15. C.Montes, Sobre ciertos tipos de bases en espacios localmente convexos. Tesis Doctoral, Sevilla 1982.

  16. C. Montes andP. Pérez, A note on basis in the sense of Abel in locally convex spaces. Bull. Soc. Roy. Sci. Liège5, 323–328 (1983).

    Google Scholar 

  17. J. Orihuela, On the equivalence of weak and Schauder bases. Arch. Math.46, 447–452 (1986).

    Google Scholar 

  18. S.Rolewicz, Metric linear spaces. Boston 1985.

  19. J. Shapiro, Extension of linear functionals onF-spaces with bases. Duke Math. J.37, 639–649 (1970).

    Google Scholar 

  20. I.Singer, Bases in Banach spaces (II). Berlin-Heidelberg-New York 1981.

  21. M. Valdivia, Absolutely convex sets in barrelled spaces. Ann. Institut Fourier21, 3–13 (1971).

    Google Scholar 

  22. M. Valdivia, Quasi-(LB)-spaces. J. London Math. Soc.35, 149–168 (1987).

    Google Scholar 

  23. A.Wilansky, Summability through functional analysis. North Holland Math. Studies85, Amsterdam 1984.

  24. K. Zeller, Approximation in Wirkfeldern von Summierungsverfahren. Arch. Math.4, 425–431 (1953).

    Google Scholar 

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Giménez, I., López, J.A. On weak and Schauder ℱ-bases in topological vector spaces. Arch. Math 51, 561–569 (1988). https://doi.org/10.1007/BF01261978

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