On basic orthogonal sequences in non-archimedean metrizable locally convex spaces (Q1599477)
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scientific article; zbMATH DE number 1753067
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On basic orthogonal sequences in non-archimedean metrizable locally convex spaces |
scientific article; zbMATH DE number 1753067 |
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On basic orthogonal sequences in non-archimedean metrizable locally convex spaces (English)
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10 June 2002
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Developing his work [Indag. Math., New Ser. 11, No. 3, 463--466 (2000; Zbl 0980.46057)], the author shows that a linearly independent sequence in a metrizable locally convex Hausdorff space \(E\) has a block sequence that is a basic orthogonal sequence in \(E\). The importance of this result may be realized from the fact that one of the unsolved problems of \(p\)-adic functional analysis is whether a complete infinite dimensional metrizable locally convex Hausdorff space of countable type has an orthogonal basis.
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non-archimedean locally convex spaces
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orthogonal sequences
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orthogonal basis
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block sequence
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compactoid
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\(p\)-adic functional analysis
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