On Universal Schauder Bases in Non-Archimedean Frechet Spaces
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Date
2004
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Canadian Mathematical Society
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Abstract
We prove that there exists a non-archimedean Frechet space U with a
basis $(u_n)$ such that any basis $(x_n)$ in a non-archimedean Frechet space X is equivalent to a subbasis
$(u_k_n)$ of $(u_n)$. Then any non-archimedean Frechet space with a basis is isomorphic to a complemented
subspace of U. Next we prove that there is no nuclear non-archimedean Frechet space
H with a basis $(h_n)$ such that any basis $(y_n)$ in a nuclear non-archimedean Frechet space Y is equivalent
to a subbasis $(h_k_n)$ of $(h_n)$.
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Keywords
Universal bases, Complemented subspaces with bases
Citation
Canad. Math. Bull. 47(2004), 108-118.