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

Robert Stegliński (2005)

Studia Mathematica

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 = (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.

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