On the quasi-equivalence of orthogonal bases in non-archimedean metrizable locally convex spaces
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Date
2002
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The Belgian Mathematical Society
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Abstract
We prove that any non-archimedean metrizable locally convex space
E with a regular orthogonal basis has the quasi-equivalence property, i.e. any two
orthogonal bases in E are quasi-equivalent. In particular, the power series spaces, the most known and important examples of non-archimedean
nuclear Frechet spaces, have the quasi-equivalence property. We also show that the
Frechet spaces: K^N, c_0xK^N, c_0^N
have the quasi-equivalence property.
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Keywords
Guasi-equivalence property, Non-archimedean Frechet spaces
Citation
Bull. Belg. Math. Soc. 9 (2002), 465-472.