Quotients of \(c_0\) and Lipschitz-homeomorphisms (Q2771477)
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scientific article; zbMATH DE number 1705548
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quotients of \(c_0\) and Lipschitz-homeomorphisms |
scientific article; zbMATH DE number 1705548 |
Statements
23 September 2003
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Lipschitz map
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Lipschitz-homeomorphic Banach spaces
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Lipschitz quotient space
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0.9181676
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0.89163905
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0.88583994
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0.8813544
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0.87781096
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0.8765765
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Quotients of \(c_0\) and Lipschitz-homeomorphisms (English)
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It is an open problem whether two separable Lipschitz-homeomorphic Banach spaces are isomorphic. In the present paper, a weaker form of this problem is investigated: Which isomorphism classes of separable Banach spaces are stable under Lipschitz-homeomorphisms? In this direction, it is proved that if the metric approximation property of the relevant space is assumed, the class of linear quotients of \(c_0\) is stable under Lipschitz-homeomorphisms. Moreover, a quantitative version of this result is obtained.
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