Generalized centers of finite sets in Banach spaces.
Generalized fatou inequalities
Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces
In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated.
Generalized Fock spaces, interpolation, multipliers, circle geometry.
By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e-Q(z), where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle C in C. We consider the problem of interpolation between two Fock spaces. If C0 and C1 are the corresponding circles, one is led to consider the pencil of circles generated by C0 and C1....
Generalized Helly spaces, continuity of monotone functions, and metrizing maps
Given an ordered metric space (in particular, a Banach lattice) E, the generalized Helly space H(E) is the set of all increasing functions from the interval [0,1] to E considered with the topology of pointwise convergence, and E is said to have property (λ) if each of these functions has only countably many points of discontinuity. The main objective of the paper is to study those ordered metric spaces C(K,E), where K is a compact space, that have property (λ). In doing so, the guiding idea comes...
Generalized induced norms
Let be a norm on the algebra of all matrices over . An interesting problem in matrix theory is that “Are there two norms and on such that for all ?” We will investigate this problem and its various aspects and will discuss some conditions under which .
Generalized Lions-Peetre methods of constants and means and operator ideals.
We establish results on interpolation of Rosenthal operators, Banach-Saks operators, Asplund operators and weakly compact operators by means of generalized Lions-Peetre methods of constants and means. Applications are presented for the K-method space generated by the Calderón-Lozanovskii space parameters.
Generalized Markuševič bases
Generalized M-norms on ordered normed spaces
L-norms and M-norms on Banach lattices, unit-norms and base norms on ordered vector spaces are well known. In this paper m- and -norms are introduced on ordered normed spaces. They generalize the notions of the M-norm and the order-unit norm, possess also some interesting properties and can be characterized by means of the constants of reproducibility of cones. In particular, the dual norm of an ordered Banach space with a closed cone turns out to be additive on the dual cone if and only if the...
Generalized modular spaces
Generalized Ulam-Hyers stability of Jensen functional equation in Šerstnev PN spaces.
Generalized-lush spaces and the Mazur-Ulam property
We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...
Generalizing the Johnson-Lindenstrauss lemma to k-dimensional affine subspaces
Let ε > 0 and 1 ≤ k ≤ n and let be affine subspaces of ℝⁿ, each of dimension at most k. Let if ε < 1, and m = O(k + log p/log(1 + ε)) if ε ≥ 1. We prove that there is a linear map such that for all 1 ≤ l ≤ p and we have ||x-y||₂ ≤ ||H(x)-H(y)||₂ ≤ (1+ε)||x-y||₂, i.e. the distance distortion is at most 1 + ε. The estimate on m is tight in terms of k and p whenever ε < 1, and is tight on ε,k,p whenever ε ≥ 1. We extend these results to embeddings into general normed spaces Y.
Generic differentiability of mappings and convex functions in Banach and locally convex spaces
Geometric characterization of L₁-spaces
The paper is devoted to a description of all real strongly facially symmetric spaces which are isometrically isomorphic to L₁-spaces. We prove that if Z is a real neutral strongly facially symmetric space such that every maximal geometric tripotent from the dual space of Z is unitary, then the space Z is isometrically isomorphic to the space L₁(Ω,Σ,μ), where (Ω,Σ,μ) is an appropriate measure space having the direct sum property.
Geometric characterizations of the Radon-Nikodym property in Banach spaces
Geometric properties of Banach spaces and metric fixed point theory.
Geometric properties of Banach spaces and the existence of nearest and farthest points.
Geometric properties of normed spaces and estimates for rectangular modulus.
Geometric properties related to the fixed point property in Banach spaces.