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, Volume 38, Issue 3, pp 333–341 | Cite as

The injective hull op an operator ideal on locally convex spaces

  • L. Franco
  • C. Piñeiro


In his book (3), Pietsch presents the problem of a direct construction of the injective hull of an operator ideal on loca. lly convex spaces. We construct the infective hull of an arbitrary operator ideal on locally convex spaces using the functor
, where
and B cover the family of all equicontinuous subsets of E'(L is the category of all locally convex spaces). If the operator ideal is bounded, we ob tain its infective hull using seminorm ideals.


Number Theory Algebraic Geometry Topological Group Operator Ideal Direct Construction 
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  1. (l).
    HORVATH, J.: Topological Vector Spaces. London: Addison Wesley 1996Google Scholar
  2. (2).
    KÖTHE, G.: Topological Vector Spaces. Berlin:Springer-Verlag 1969Google Scholar
  3. (3).
    PIETSCH, A.: Operator ideals Amsterdam-New York-Oxford North Holland 1980Google Scholar
  4. (4).
    PIETSCH, A.: Theorie der Operatorenideale. Friedrich-Schiler Universität Jena (1972)Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • L. Franco
    • 1
  • C. Piñeiro
    • 1
  1. 1.Departamento de Teoria de Funciones Facultad de MatemáticasUniversidad de SevillaSevilla 12.España

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