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]

top of page | contact us | social media | privacy | site map