Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely
Volume 170 / 2005
Studia Mathematica 170 (2005), 283-295
MSC: 43A35, 43A40, 46A04.
DOI: 10.4064/sm170-3-5
Abstract
It is proved that every real metrizable locally convex space which is not nuclear contains a closed additive subgroup $K$ such that the quotient group $G=(\mathop{\rm span} K)/K$ admits a non-trivial continuous positive definite function, but no non-trivial continuous character. Consequently, $G$ cannot satisfy any form of the Bochner theorem.
