Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
- 46A25: Reflexivity and semi-reflexivity
- 46A40: Ordered topological linear spaces, vector lattices
- 91A44: Games involving topology or set theory
- 91A80: Applications of game theory
- 46A55: Convex sets in topological linear spaces; Choquet theory
- 47B65: Positive operators and order-bounded operators
- 60B05: Probability measures on topological spaces
- 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
- 54C20: Extension of maps
- 46B42: Banach lattices
- 46B40: Ordered normed spaces
- 46B09: Probabilistic methods in Banach space theory
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
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm191-2-2