Generalized Cauchy functional equation and characterizations of inner product spaces. (Summary).
Geometría de gramianos en el espacio de Hilbert.
The purpose of the Part I of this paper is to develop the geometry of Gram's determinants in Hilbert space. In Parts II and III a generalization is given of the Pythagorean theorem and triangular inequality for finite vector families.
Grüss type inequalities for forward difference of vectors in inner product spaces.
Hilberträume mit amorphen basen
History, generalizations and unified treatment of two Ostrowski's inequalities.
Hyers-Ulam constants of Hilbert spaces
The best constant in the Hyers-Ulam theorem on isometric approximation in Hilbert spaces is equal to the Jung constant of the space.
Improvement of Jensen-Steffensen's inequality for superquadratic functions.
Inequalities involving the inner product.
Infinite dimensional extension of A. P. Calderòn's theorem on positive semidefinite biquadratic forms.
Infinite-dimensional bicomplex Hilbert spaces.
Isomorphic characterizations of Hilbert spaces by orthogonal series with vector valued coefficients
Isomorphic characterizations of inner product spaces by orthogonal series with vector valued coefficients
Linear algebra and differential geometry on abstract Hilbert space.
Local and global -cone porosity
Locally constant functions
Let X be a compact Hausdorff space and M a metric space. is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of as a normed linear space. We also build three first countable Eberlein...
Lower bounds on products of correlation coefficients.
MD-numbers and asymptotic MD-numbers of operators.
Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie
We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.
Metric entropy of convex hulls in Hilbert spaces
Let T be a precompact subset of a Hilbert space. We estimate the metric entropy of co(T), the convex hull of T, by quantities originating in the theory of majorizing measures. In a similar way, estimates of the Gelfand width are provided. As an application we get upper bounds for the entropy of co(T), , , by functions of the ’s only. This partially answers a question raised by K. Ball and A. Pajor (cf. [1]). Our estimates turn out to be optimal in the case of slowly decreasing sequences .
Metrics in the set of partial isometries with finite rank
Let be the set of partial isometries with finite rank of an infinite dimensional Hilbert space . We show that is a smooth submanifold of the Hilbert space of Hilbert-Schmidt operators of and that each connected component is the set , which consists of all partial isometries of rank . Furthermore, is a homogeneous space of , where is the classical Banach-Lie group of unitary operators of , which are Hilbert-Schmidt perturbations of the identity. We introduce two Riemannian metrics...