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

• Autorzy: Robert Stegliński
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 43A40: Character groups and dual objects
• 43A35: Positive definite functions on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 3
• Strony: 283-295

Daty

wydano

2005

Twórcy

autor

Robert Stegliński

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

Identyfikatory

DOI

10.4064/sm170-3-5