Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is closely related to the classical problem of determining whether or not there is a discontinuous translation invariant linear functional on X. As a matter of fact L¹(G) does not carry a unique Banach space topology that makes translations continuous, but translations almost determine the Banach space topology on X. Moreover, if G is connected and compact and 1 < p < ∞, then $L^{p}(G)$ carries a unique Banach space topology that makes translations continuous.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
163-173
Opis fizyczny
Daty
wydano
2002
Twórcy
autor
- Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
autor
- Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 GRANADA, Spain
autor
- Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 GRANADA, Spain
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm150-2-5