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Extensions of the representation theorems of Riesz and Fréchet

João C. Prandini (1993)

Mathematica Bohemica

We present two types of representation theorems: one for linear continuous operators on space of Banach valued regulated functions of several real variables and the other for bilinear continuous operators on cartesian products of spaces of regulated functions of a real variable taking values on Banach spaces. We use generalizations of the notions of functions of bounded variation in the sense of Vitali and Fréchet and the Riemann-Stieltjes-Dushnik or interior integral. A few applications using geometry...

Finite codimensional linear isometries on spaces of differentiable and Lipschitz functions

Hironao Koshimizu (2011)

Open Mathematics

We characterize finite codimensional linear isometries on two spaces, C (n)[0; 1] and Lip [0; 1], where C (n)[0; 1] is the Banach space of n-times continuously differentiable functions on [0; 1] and Lip [0; 1] is the Banach space of Lipschitz continuous functions on [0; 1]. We will see they are exactly surjective isometries. Also, we show that C (n)[0; 1] and Lip [0; 1] admit neither isometric shifts nor backward shifts.

Fonctionnelles analytiques sur certains espaces de Banach

Gérard Cœuré (1971)

Annales de l'institut Fourier

Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène E , au sens de Katznelson, de L 1 ( π ) muni de la topologie engendrée par les semi-normes portées par les compacts de E , est bornologique.

Funciones unimodulares y acotación uniforme.

J. Fernández, S. Hui, Harold S. Shapiro (1989)

Publicacions Matemàtiques

In this paper we study the role that unimodular functions play in deciding the uniform boundedness of sets of continuous linear functionals on various function spaces. For instance, inner functions are a UBD-set in H∞ with the weak-star topology.

Generalized Helly spaces, continuity of monotone functions, and metrizing maps

Lech Drewnowski, Artur Michalak (2008)

Fundamenta Mathematicae

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 Hölder type spaces of harmonic functions in the unit ball and half space

Alexey Karapetyants, Joel Esteban Restrepo (2020)

Czechoslovak Mathematical Journal

We study spaces of Hölder type functions harmonic in the unit ball and half space with some smoothness conditions up to the boundary. The first type is the Hölder type space of harmonic functions with prescribed modulus of continuity ω = ω ( h ) and the second is the variable exponent harmonic Hölder space with the continuity modulus | h | λ ( · ) . We give a characterization of functions in these spaces in terms of the behavior of their derivatives near the boundary.

Generalized weak peripheral multiplicativity in algebras of Lipschitz functions

Antonio Jiménez-Vargas, Kristopher Lee, Aaron Luttman, Moisés Villegas-Vallecillos (2013)

Open Mathematics

Let (X, d X) and (Y,d Y) be pointed compact metric spaces with distinguished base points e X and e Y. The Banach algebra of all 𝕂 -valued Lipschitz functions on X - where 𝕂 is either‒or ℝ - that map the base point e X to 0 is denoted by Lip0(X). The peripheral range of a function f ∈ Lip0(X) is the set Ranµ(f) = f(x): |f(x)| = ‖f‖∞ of range values of maximum modulus. We prove that if T 1, T 2: Lip0(X) → Lip0(Y) and S 1, S 2: Lip0(X) → Lip0(X) are surjective mappings such that R a n π ( T 1 ( f ) T 2 ( g ) ) ∩ R a n π ( S 1 ( f ) S 2 ( g ) ) ≠ ∅ for all f, g ∈ Lip0(X),...

Currently displaying 141 – 160 of 495