21 Übersetzungen
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Anwendungsbeispiele Englisch
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- The basis problem was posed by Stefan Banach in his book, "Theory of Linear Operators". Banach asked whether every separable Banach space has a Schauder basis.
- Franklin proved in 1928 that this system is a Schauder basis for "C"(...).
- On 6 November 1936, he posed the "basis problem" of determining whether every Banach space has a Schauder basis, with Mazur promising a "live goose" as a reward: 37 years later and in a ceremony that was broadcast throughout Poland, Mazur awarded a live goose to Per Enflo for constructing a counter-example.
- Banach spaces with a Schauder basis are necessarily separable, because the countable set of finite linear combinations with rational coefficients (say) is dense.
- With Bernard Maurey he resolved the "unconditional basic sequence problem" in 1992, showing that not every infinite-dimensional Banach space has an infinite-dimensional subspace that admits an unconditional Schauder basis.
- In mathematics, a Schauder basis or countable basis is similar to the usual (Hamel) basis of a vector space; the difference is that Hamel bases use linear combinations that are finite sums, while for Schauder bases they may be infinite sums.
- The Walsh system (in Walsh-Paley numeration) forms a Schauder basis in [...] , [...].
© dict.cc English-German dictionary 2024
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