- Tytuł:
- Operators on $C(ω^α)$ which do not preserve $C(ω^α)$
- Autorzy:
- Alspach, Dale
- Powiązania:
- https://bibliotekanauki.pl/articles/1205439.pdf
- Data publikacji:
- 1997
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
ordinal index
Szlenk index
Banach space of continuous functions - Opis:
- It is shown that if α,ζ are ordinals such that 1 ≤ ζ < α < ζω, then there is an operator from $C(ω^{ω^α})$ onto itself such that if Y is a subspace of $C(ω^{ω^α})$ which is isomorphic to $C(ω^{ω^α})$, then the operator is not an isomorphism on Y. This contrasts with a result of J. Bourgain that implies that there are uncountably many ordinals α for which for any operator from $C(ω^{ω^α})$ onto itself there is a subspace of $C(ω^{ω^α})$ which is isomorphic to $C(ω^{ω^α})$ on which the operator is an isomorphism.
- Źródło:
-
Fundamenta Mathematicae; 1997, 153, 1; 81-98
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł