The Ramsey theorem and complemented basic sequences in Fréchet spaces with absolute finite-dimensional decompositions (Q1109279)
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scientific article; zbMATH DE number 4069548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Ramsey theorem and complemented basic sequences in Fréchet spaces with absolute finite-dimensional decompositions |
scientific article; zbMATH DE number 4069548 |
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The Ramsey theorem and complemented basic sequences in Fréchet spaces with absolute finite-dimensional decompositions (English)
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1989
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In Arch. Math. 38, 138-150 (1982; Zbl 0494.46004) \textit{Ed Dubinsky} proved that a nuclear Fréchet space with a decomposition into two- dimensional blocks has a complemented basic sequence. In this paper a short proof of Dubinsky's result is given. This proof reveals the combinatorial nature of the result, removes the assumption of nuclearity and shows the difficult points in trying to generalize the result to finite-dimensional decompositions with blocks of higher dimension.
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nuclear Fréchet space with a decomposition into two-dimensional blocks
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complemented basic sequence
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Ramsey theorem
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