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## Studia Mathematica

2009 | 191 | 2 | 123-150
Tytuł artykułu

### Extenders for vector-valued functions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a subset A of a topological space X, a locally convex space Y, and a family ℂ of subsets of Y we study the problem of the existence of a linear ℂ-extender $u: C_{∞}(A,Y) → C_{∞}(X,Y)$, which is a linear operator extending bounded continuous functions f: A → C ⊂ Y, C ∈ ℂ, to bounded continuous functions f̅ = u(f): X → C ⊂ Y. Two necessary conditions for the existence of such an extender are found in terms of a topological game, which is a modification of the classical strong Choquet game. The results obtained allow us to characterize reflexive Banach spaces as the only normed spaces Y such that for every closed subset A of a GO-space X there is a ℂ-extender $u: C_{∞}(A,Y) → C_{∞}(X,Y)$ for the family ℂ of closed convex subsets of Y. Also we obtain a characterization of Polish spaces and of weakly sequentially complete Banach lattices in terms of extenders.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
123-150
Opis fizyczny
Daty
wydano
2009
Twórcy
autor
• Department of Functional Analysis, Ya. Pidstryhach Institute for Applied Problems, of Mechanics and Mathematics, Naukova 3b, Lviv, Ukraine
autor
• Instytut Matematyki, Akademia Świętokrzyska, 25-406 Kielce, Poland
• Department of Mathematics, Ivan Franko National University of Lviv, Universytetska 1, 79000, Lviv, Ukraine
autor
• Faculty of Economics, Takasaki City University of Economics, 1300 Kaminamie, Takasaki, Gunma 370-0801, Japan
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