On Besselian Schauder bases in \(\ell_ p(E)\) (Q788237)
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scientific article; zbMATH DE number 3842483
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Besselian Schauder bases in \(\ell_ p(E)\) |
scientific article; zbMATH DE number 3842483 |
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On Besselian Schauder bases in \(\ell_ p(E)\) (English)
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1984
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By complex interpolation and tensor products, Schauder bases are constructed of the Banach sequence spaces \(\ell_ p(E)\). In a general result, we study the Besselian property of the basis, and if E is assumed to be the \(L_ p\) (Lebesgue) and \(S_ p\) (von Neumann-Schatten) space, we obtain inequalities for the coefficient functionals associated to the basis which generalise other results given by Hausdorff-Young and Gohberg-Marcus. Finally, we construct non-Besselian and conditional bases of \(\ell_ p(E)\).
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Besselian bases
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complex interpolation
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tensor products
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Schauder bases
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(von Neumann-Schatten) space
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