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Über die Einbettung der nuklearen Räume in (s) A

In: Contributions to Functional Analysis

Author

Listed:
  • Takako Kōmura
  • Yukio Kōmura

Abstract

Zusammenfassung In dieser Arbeit geben wir eine neue Charakterisierung der nuklearen Räume an: Ein lokal konvexer Raum ist dann und nur dann nuklear, wenn er isomorph zu einem Teilraum des Produkts (s) A des Raumes (s) aller schnell fallenden Folgen ist. (A bezeichnet eine geeignete Indexmenge.) Damit haben wir gleichzeitig bewiesen, daß jeder nukleare (F)-Raum in den Raum E (R 1) aller beliebig oft differenzierbaren Funktionen auf R 1 isomorph eingebettet werden kann. Dieses Problem stammt von Grothendieck [3], und in einigen speziellen Fällen waren positive Antworten bekannt, insbesondere im Fall von nuklearen (F)-Räumen mit Basis, d. h. im Fall von nuklearen, vollkommenen (F)-Räumen (vgl. [1], [3]).

Suggested Citation

  • Takako Kōmura & Yukio Kōmura, 1966. "Über die Einbettung der nuklearen Räume in (s) A," Springer Books, in: Contributions to Functional Analysis, pages 284-288, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-85997-7_18
    DOI: 10.1007/978-3-642-85997-7_18
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