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The isometric approximation problem in \(B(\ell^ 1(\Gamma{}), C(\Omega{}))\) - MaRDI portal

The isometric approximation problem in \(B(\ell^ 1(\Gamma{}), C(\Omega{}))\) (Q1191682)

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scientific article; zbMATH DE number 62541
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English
The isometric approximation problem in \(B(\ell^ 1(\Gamma{}), C(\Omega{}))\)
scientific article; zbMATH DE number 62541

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    The isometric approximation problem in \(B(\ell^ 1(\Gamma{}), C(\Omega{}))\) (English)
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    27 September 1992
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    Theorem: The isometric approximation problem on \(B(\ell_ 1(\Gamma),C(\Omega))\) is negative if and only if \(\ell_ 1(\Gamma)\) can be imbedded into \(C(\Omega)\) almost isometrically. Apparently all the definitions can be found in another paper by the author, ``Isometric approximations from uniformly smooth spaces into \(\ell_ \infty(\Gamma)\) type spaces'', Acta Math. Sci. 9, No. 1, 27-32 (1989; Zbl 0716.46025)].
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    \(\varepsilon\)-isometry
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    almost isometric embedding
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    isometric approximation problem
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