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On Quotients of Non-Archimedean Köthe Spaces

  Published:2007-03-01
 Printed: Mar 2007
  • Wiesław Śliwa
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Abstract

We show that there exists a non-archimedean Fr\'echet-Montel space $W$ with a basis and with a continuous norm such that any non-archimedean Fr\'echet space of countable type is isomorphic to a quotient of $W$. We also prove that any non-archimedean nuclear Fr\'echet space is isomorphic to a quotient of some non-archimedean nuclear Fr\'echet space with a basis and with a continuous norm.
Keywords: Non-archimedean Köthe spaces, nuclear Fréchet spaces, pseudo-bases Non-archimedean Köthe spaces, nuclear Fréchet spaces, pseudo-bases
MSC Classifications: 46S10, 46A45 show english descriptions Functional analysis over fields other than ${\bf R}$ or ${\bf C}$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
Sequence spaces (including Kothe sequence spaces) [See also 46B45]
46S10 - Functional analysis over fields other than ${\bf R}$ or ${\bf C}$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]
46A45 - Sequence spaces (including Kothe sequence spaces) [See also 46B45]
 

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