Banach spaces which embed into their dual
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz representation theorem.
Banach-Euclidean four-point properties
Bessel and Grüss type inequalities in inner product modules over Banach -algebras.
Bilipschitz mappings and strong weights.
Bochner property in Banach spaces
Bootstrapping Kirszbraun's extension theorem
We show how Kirszbraun's theorem on extending Lipschitz mappings in Hilbert space implies its own generalization. There is a continuous extension operator preserving the Lipschitz constant of every mapping.
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.
Cauchy multiplication and periodic functions (mod r).
We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
C-Complete Systems In Normed Spaces
Central points of convex sets
Characteristic matrix functions on Wachs spaces, I. (Livsits definition).
Characterization of Bessel sequences.
Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.
Characterizations of inner product spaces by strongly convex functions.
Characterizations of inner product spaces through an isosceles trapezoid property
Generalizing a property of isosceles trapezoids in the real plane into real normed spaces, a couple of characterizations of inner product spaces (i.p.s) are obtained.
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
Circumcenters in real normed spaces
The study of circumcenters in different types of triangles in real normed spaces gives new characterizations of inner product spaces.