Sous-espaces hilbertiens d’espaces vectoriels topologiques et noyaux associés (Noyaux reproduisants)

On L. Schwartz's Boundedness Condition for Kernels

“…As it was shown in [18], the natural framework for studying hermitian kernels is given by Kreȋn spaces and for this reason we briefly discuss the necessary terminology.…”

“…for all f, g ∈ F 0 (X, H) (see Proposition 38, [18]), it follows that N L is a subset of the isotropic subspace N K of the inner product space (…”

“…We also related these constructions with the GNS representations of * -algebras, an issue of some recent interest in quantum field theory with indefinite metric ( [2], [14], [13], [19]). The conditions on the kernel turned out to be of a type considered previously by L. Schwartz in [18] in the related matter of characterizing those hermitian kernels that are in the real linear space generated by positive definite kernels. These boundedness conditions are rather difficult to be verified, see [2], [13], and their nature is quite obscure, see [19].…”

Étude et convergence de fonctions «spline» complexes

“…De la proposition 2.4 de [8] et de la positivité du noyau E m9 on déduit que E m est continu sur l'intérieur de Q.…”

Brève communication. Un théorème de caractérisation de certains sous-espaces hilbertiens de $l_1$

“…[3]) est un espace de Hilbert inclus dans E tel que l'injection canonique de h dans E soit continue :…”