In this article we consider the sequences of sample and population covariance operators for a sequence of arrays of Hilbertian random elements. Then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

in this article we consider the sequences of sample and population covariance operators for a sequence of arrays of hilbertian random elements. then under the assumptions that sequences of the covariance operators norm are uniformly bounded and the sequences of the principal component scores are uniformly sumable, we prove that the convergence of the sequences of covariance operators would impl...

This paper is devoted to some variants of the Hilbert specialization property. For example, the RG-hilbertian property (for a field K), which arose in connection with the Inverse Galois Problem, requires that the specialization property holds solely for extensions of K(T ) that are Galois and regular over K. We show that fields inductively obtained from a real hilbertian field by adjoining real...

In this paper, we suggest a construction of determinant lines of finitely generated Hilbertian modules over finite von Neumann algebras. Nonzero elements of the determinant lines can be viewed as volume forms on the Hilbertian modules. Using this, we study both L combinatorial and L analytic torsion invariants associated to flat Hilbertian bundles over compact polyhedra and manifolds; we view t...

A field K is 0-Hilbertian if K 6= ⋃ni=1 φi(K) for any collection of rational functions φi of degree at least 2, i = 1, . . . ,m. Corvaja and Zannier [CoZ] give an elementary construction for a 0-Hilbertian field that isn’t Hilbertian. There is an obvious generalization of the notion of 0-Hilbertian to g-Hilbertian. Guralnick-Thompson and Liebeck-Saxl have given a partial classification of monod...

Given a finite set S of places of a number field, we prove that the field of totally S-adic algebraic numbers is not Hilbertian. The field of totally real algebraic numbers Qtr, the field of totally p-adic algebraic numbers Qtot,p, and, more generally, fields of totally S-adic algebraic numbers Qtot,S, where S is a finite set of places of Q, play an important role in number theory and Galois th...

In this paper, we discuss elliptically contoured distribution for random variables defined on a separable Hilbert space. It is a generalization of the multivariate elliptically contoured distribution to distributions on infinite dimensional spaces. Some theoretical properties of the Hilbertian elliptically contoured distribution are discussed, examples on functional data are investigated to ill...

In this article we investigate the field of Hilbertian metrics on probability measures. Since they are very versatile and can therefore be applied in various problems they are of great interest in kernel methods. Quit recently Topsøe and Fuglede introduced a family of Hilbertian metrics on probability measures. We give basic properties of the Hilbertian metrics of this family and other used met...