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manuscripta mathematica

, Volume 22, Issue 1, pp 7–12 | Cite as

Über die Tonneliertheit von lokalkonvexen Tensorprodukten

  • Ralf Hollstein
Article

Abstract

It is known that the inductive tensor product of two barrelled spaces is barrelled and that the projective tensor product of two barrelled metrizable spaces or barrelled (DF)-spaces is barrelled. In this note it will be shown by a counterexample that the projective tensor product E⊕ΠF of two barrelled spaces E and F in general is not barrelled, even if E is (DF)-Montel-space and F (F)-Montel-space. Furthermore we show that the ε-tensor product of two (B)-spaces in general is not barrelled. It follows from the fact that an (F)-space E is nuclear if and only if the ε-tensor product E⊕ɛl4 is barrelled.

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Literatur

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Copyright information

© Springer-Verlag 1977

Authors and Affiliations

  • Ralf Hollstein
    • 1
  1. 1.Fachbereich 17 (Mathematik) der Gesamthochschule PaderbornPaderborn

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