Perfectness of certain subsemigroups of a perfect semigroup.
Positive Definite Functions on Abelian Semigroups.
Positive Definite Functions on the Heisenberg Group.
Positive Definite Kernels on the Complex Hilbert Sphere.
Positive Q-matrices of graphs
The Q-matrix of a connected graph = (V,E) is , where ∂(x,y) is the graph distance. Let q() be the range of q ∈ (-1,1) for which the Q-matrix is strictly positive. We obtain a sufficient condition for the equality q(̃) = q() where ̃ is an extension of a finite graph by joining a square. Some concrete examples are discussed.
Positive-definite kernels, length functions on groups and a noncommutative von Neumann inequality
Property (T) and groups
We show that each group in a class of finitely generated groups introduced in [2] and [3] has Kazhdan’s property (T), and calculate the exact Kazhdan constant of with respect to its natural set of generators. These are the first infinite groups shown to have property (T) without making essential use of the theory of representations of linear groups, and the first infinite groups with property (T) for which the exact Kazhdan constant has been calculated. These groups therefore provide answers...
Property T for discrete groups in terms of their regular representation.
Property (T) for ... Factors and unitary representations of Kazhdan groups.
Propriétés des applications quadratiques d'un espace de Hilbert dans un espace vectoriel. Applications à la théorie spectrale des opérateurs normaux et à l'image numérique d'un opérateur
Pull-back properties of moment functions and a generalization of Bochner-Weil' s theorem.