Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 335p-350p
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.
* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.