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On Completions of LB-spaces of Moscatelli type

Sobre las completaciones de espacios LB de tipo Moscatelli

Abstract

We first present a class of LF-spaces, extending the class of LF-spaces of Moscatelli type, for which regularity implies completeness. Then we utilize the obtained results to describe the completions of LB-spaces of Moscatelli type. In particular, we prove that the completions of LB-spaces of that type are again LB-spaces.

Resumen

Presentamos primero una clase de espacios LF, que extiende los espacios LF de tipo Moscatelli, para la cual la regularidad del límite inductivo implica la completitud. A continuación utilizamos los resultados obtenidos para describir la completación de los espacios LB de tipo Moscatelli usual. En particular, demostramos que la completación de un espacio LB de ese tipo es también un espacio LB.

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References

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    Bonet, J. andDierolf, S., (1989). On LB-spaces of Moscatelli Type.Doga T U J. Math.,13, 9–33.

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    Bonet, J., Dierolf, S. and Fernández, C., (1992). On two classes of LF-Spaces.Port. Math.,49.

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    Mel’endez, Y., (1990) Inductive limits of Moscatelli type for locally convex spaces. Dissertation University of Extemadura, Badajoz

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    Pasynkov, B. A., (1969). On topological groups,Soviet. Math. Doklady,10, 1115–1118.

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Author information

Correspondence to Susanne Dierolf.

Additional information

Dedicated to the Memory of Walter Roelcke, doctoral promotor of the first author

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Dierolf, S., Kuß, P. On Completions of LB-spaces of Moscatelli type. Rev. R. Acad. Cien. Serie A. Mat. 102, 205–209 (2008). https://doi.org/10.1007/BF03191821

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Keywords

  • LB-spaces
  • LF-spaces
  • spaces of Moscatelli type
  • regular
  • complete

Mathematics Subject Classifications

  • 46A13