Geodesic
Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps
Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 335-350.

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The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis. If a Banach space E cannot be decomposed into a direct sum of separable and reflexive subspaces, then there exists a normed space Z and a linear continuous bijective operator T : E → Z such that T^(−1) is not a Borel map.
Keywords: Banach Space, Borel Map 
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     title = {Decomposition of {Banach} {Space} into a {Direct} {Sum} of {Separable} and {Reflexive} {Subspaces} and {Borel} {Maps}},
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Plichko, Anatolij. Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps. Serdica Mathematical Journal, Tome 23 (1997) no. 3-4, pp. 335-350. http://geodesic.mathdoc.fr/item/SMJ2_1997_23_3-4_a9/