Espaces de Krein et index des systèmes hamiltoniens
Espaces du type Sobolev sur un espace de Hilbert complexe
Espaces hilbertiens symétriques et produits tensoriels continus
Espacios con producto interior probabilístico.
Probabilistic inner product spaces are studied with detail.
Espacios de producto interno (II).
Among normal linear spaces, the inner product spaces (i.p.s.) are particularly interesting. Many characterizations of i.p.s. among linear spaces are known using various functional equations. Three functional equations characterizations of i.p.s. are based on the Frchet condition, the Jordan and von Neumann identity and the Ptolemaic inequality respectively. The object of this paper is to solve generalizations of these functional equations.
Étude d'un problème de continuité lié à l'hypothèse de Riemann
Cet article est consacré à l’étude d’un problème lié au critère de Beurling Nyman sur l’hypothèse de Riemann. On y étudie la continuité de la projection de la fonction indicatrice de l’intervalle sur un sous-espace vectoriel variable de l’ensemble des fonctions dont le carré est intégrable sur la demi-droite réelle, engendré par des fonctions dilatées de la fonction partie fractionnaire. Plus généralement, étant un élément fixé d’un espace de Hilbert , on étudie l’application qui à un convexe...
Every Frame is a Sum of Three (But Not Two) Orthonormal Bases-and Other Frame Representations.
Exponentially bounded indefinite functions.
Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric. I.
Extensions of nonexpansive mappings in the Hilbert ball with the hyperbolic metric. II.
Extensions of two classic kinds of Wachs space operators
Failure of the Factor Theorem for Borel pre-Hilbert spaces
In every infinite-dimensional Fréchet space X, we construct a linear subspace E such that E is an -subset of X and contains a retract R so that is not homeomorphic to . This shows that Toruńczyk’s Factor Theorem fails in the Borel case.
Finite-dimensional Hilbert -modules.
Fonctions «spline» et noyaux reproduisants d'Aronszajn-Bergman
Frame functions and completeness of inner product spaces
Frame functions, signed measures and completeness of inner product spaces
Generalized atomic subspaces for operators in Hilbert spaces
We introduce the notion of a -atomic subspace for a bounded linear operator and construct several useful resolutions of the identity operator on a Hilbert space using the theory of -fusion frames. Also, we shall describe the concept of frame operator for a pair of -fusion Bessel sequences and some of their properties.
Generalized Cauchy functional equation and characterizations of inner product spaces.
Generalized Cauchy functional equation and characterizations of inner product spaces. (Summary).
Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras
The notion of a -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then...