Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely
Studia Mathematica (2005)
- Volume: 170, Issue: 3, page 283-295
- ISSN: 0039-3223
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topRobert Stegliński. "Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely." Studia Mathematica 170.3 (2005): 283-295. <http://eudml.org/doc/284998>.
@article{RobertStegliński2005,
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 = (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.},
author = {Robert Stegliński},
journal = {Studia Mathematica},
keywords = {Bochner theorem; nuclear spaces; positive definite functions; group characters},
language = {eng},
number = {3},
pages = {283-295},
title = {Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely},
url = {http://eudml.org/doc/284998},
volume = {170},
year = {2005},
}
TY - JOUR
AU - Robert Stegliński
TI - Quotient groups of non-nuclear spaces for which the Bochner theorem fails completely
JO - Studia Mathematica
PY - 2005
VL - 170
IS - 3
SP - 283
EP - 295
AB - 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.
LA - eng
KW - Bochner theorem; nuclear spaces; positive definite functions; group characters
UR - http://eudml.org/doc/284998
ER -
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