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- W1990757038 abstract "Abstract It is known that any non-archimedean Fréchet space of countable type is isomorphic to a subspace of . In this paper we prove that there exists a non-archimedean Fréchet space U with a basis ( u n ) such that any basis ( x n ) in a non-archimedean Fréchet space X is equivalent to a subbasis ( u k n ) of ( u n ). Then any non-archimedean Fréchet space with a basis is isomorphic to a complemented subspace of U . In contrast to this, we show that a non-archimedean Fréchet space X with a basis ( x n ) is isomorphic to a complemented subspace of if and only if X is isomorphic to one of the following spaces: c 0 , c 0 × . Finally, we prove that there is no nuclear non-archimedean Fréchet space H with a basis ( h n ) such that any basis ( y n ) in a nuclear non-archimedean Fréchet space Y is equivalent to a subbasis ( h k n ) of ( h n )." @default.
- W1990757038 created "2016-06-24" @default.
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- W1990757038 date "2004-03-01" @default.
- W1990757038 modified "2023-10-18" @default.
- W1990757038 title "On Universal Schauder Bases in Non-Archimedean Fréchet Spaces" @default.
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- W1990757038 doi "https://doi.org/10.4153/cmb-2004-012-2" @default.
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