1. Twisted sums of c0(I).
- Author
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Castillo, Jessú M.F. and Salguero Alarcón, Alberto
- Subjects
- *
BANACH spaces , *FUNCTION spaces , *PROBLEM solving , *SEQUENCE spaces , *COMPACT spaces (Topology) , *POLYHEDRAL functions - 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]
- Published
- 2023
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