Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely

Volume 170 / 2005

Robert Stegliński Studia Mathematica 170 (2005), 283-295 MSC: 43A35, 43A40, 46A04. DOI: 10.4064/sm170-3-5


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.


  • Robert SteglińskiFaculty of Mathematics
    Łódź University
    Banacha 22
    90-238 Łódź, Poland

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