Subspaces of \(\ell_{1}\) satisfying Grothendieck's theorem (Q1700036)
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scientific article; zbMATH DE number 6843730
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Subspaces of \(\ell_{1}\) satisfying Grothendieck's theorem |
scientific article; zbMATH DE number 6843730 |
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Subspaces of \(\ell_{1}\) satisfying Grothendieck's theorem (English)
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26 February 2018
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Recall that a quadratic form on a Banach space \(X\) is a map \(q:X \rightarrow \mathbb{R}\) such that there exists a continuous bilinear form \(b:X \times X \rightarrow \mathbb{R}\) for which \(q(x) = b(x, x)\). In the present paper, a characterization of Grothendieck subspaces of \(\ell_1\) is given in terms of the extension of nonnegative quadratic forms to the whole space \(\ell_1\).
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Grothendieck's theorem
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quadratic form
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