Back to Search
Start Over
Twisted sums of c0(I).
- Source :
-
QM - Quaestiones Mathematicae . Nov2023, Vol. 46 Issue 11, p2339-2354. 16p. - Publication Year :
- 2023
-
Abstract
- We study in this paper a few remarkable properties of twisted sums Z(κ, X) of c0(κ) and a Banach space X. We first prove a representation theorem for such twisted sums from which we will obtain, among others, the following: (a) twisted sums of c0(κ) and c0(I) are either subspaces of ℓ∞(κ) or contain a complemented copy of c0(κ+); (b) under the hypothesis [p = c], when K is either a suitable Corson compact, a separable Rosenthal compact or a scattered compact of finite height, there is a twisted sum of c0 and C(K) that is not isomorphic to a space of continuous functions; (c) all twisted sums Z(κ, X) are isomorphically Lindenstrauss spaces when X is a Lindenstrauss space; (d) all twisted sums Z(κ, X) are isomorphically polyhedral when X is a polyhedral space with a σ-discrete boundary, which solves a problem of Castillo and Papini. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16073606
- Volume :
- 46
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- QM - Quaestiones Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 172994730
- Full Text :
- https://doi.org/10.2989/16073606.2022.2146546