Geodesic
Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely
Robert Stegliński1
1Faculty of Mathematics Łódź University Banacha 22 90-238 Łódź, Poland
Studia Mathematica, Tome 170 (2005) no. 3, pp. 283-295
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm170-3-5
Keywords: proved every real metrizable locally convex space which nuclear contains closed additive subgroup quotient group mathop span admits non trivial continuous positive definite function non trivial continuous character consequently cannot satisfy form bochner theorem

Robert Stegliński  1

1 Faculty of Mathematics Łódź University Banacha 22 90-238 Łódź, Poland 
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Robert Stegliński. Quotient groups of non-nuclear spaces
for which the Bochner theorem fails completely. Studia Mathematica, Tome 170 (2005) no. 3, pp. 283-295. doi: 10.4064/sm170-3-5

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