2022/04/01 by Jesús M. F. Castillo, Castillo, Jesús M. F., Alberto Salguero Alarcón +1
Computer Science · Mathematics · #46B20 #46E15 #46M18 #54D30 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2204.01704
openalex publication_date 2022/04/01 · openalex created_date 2022/04/28 · openalex updated_date 2026/07/28
The paper studies properties of twisted sums of a Banach space X with c0(κ). We first prove a representation theorem for such twisted sums from which we will obtain, among others, the following: (a) twisted sums of c0(I) and c0(κ) are either subspaces of ℓ_∞(κ) or trivial on a copy of c0(κ+); (b) under the hypothesis [\mathfrak p = \mathfrak 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 C(K) with c0(κ) that is not isomorphic to a space of continuous functions; (c) all such twisted sums are Lindenstrauss spaces when X is a Lindenstrauss space and G-spaces when X=C(K) with K convex, which shows tat a result of Benyamini is optimal; (d) they are isomorphically polyhedral when X is a polyhedral space with property (⋆), which solves a problem of Castillo and Papini.