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Displaying similar documents to “Summable families in nuclear groups”

On nuclear maps between spaces of ultradiferentiables jets of Roumieu type.

Jean Schmets, Manuel Valdivia (2003)

RACSAM

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Si K es un compacto no vacío en R, damos una condición suficiente para que la inyección canónica de ε(K) en ε(K) sea nuclear. Consideramos el caso mixto y obtenemos la existencia de un operador de extensión nuclear de ε(F) en ε(R) donde F es un subconjunto cerrado propio de R y A y D son discos de Banach adecuados. Finalmente aplicamos este último resultado al caso Borel, es decir cuando F = {0}.

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

Robert Stegliński (2005)

Studia Mathematica

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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 = (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.