Boule minima contenant une partie bornée de l'espace
Bounded linear regularity, strong CHIP, and CHIP are distinct properties.
Bounded operators on non-Archimedian orthomodular spaces
-algebras of operators in non-archimedean Hilbert spaces
We show several examples of n.av̇alued fields with involution. Then, by means of a field of this kind, we introduce “n.aḢilbert spaces” in which the norm comes from a certain hermitian sesquilinear form. We study these spaces and the algebra of bounded operators which are defined on them and have an adjoint. Essential differences with respect to the usual case are observed.
Characterizations of inner product structures involving the radius of the inscribed or circumscribed circumference
We define the radius of the inscribed and circumscribed circumferences in a triangle located in a real normed space and we obtain new characterizations of inner product spaces.
Characterizing Hilbert space topology
Conditionally positive definite functions on linear spaces
Curvatures and Curves in Hilbert Space.
Description of all regular cones in a Hilbert space.
Diagonals of Self-adjoint Operators with Finite Spectrum
Given a finite set X⊆ ℝ we characterize the diagonals of self-adjoint operators with spectrum X. Our result extends the Schur-Horn theorem from a finite-dimensional setting to an infinite-dimensional Hilbert space analogous to Kadison's theorem for orthogonal projections (2002) and the second author's result for operators with three-point spectrum (2013).
Dirac structures on Hilbert spaces.
Ensembles absorbants pour les classes projectives
We prove the existence, in the Hilbert space, of an absorbing set for the nth projective class.
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.
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.
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.
Fonctions «spline» et noyaux reproduisants d'Aronszajn-Bergman
Frame functions, signed measures and completeness of inner product spaces
Generalized Cauchy functional equation and characterizations of inner product spaces.