Shellable weakly compact subsets of C[0,1]

2016/03/17 by J. López-Abad, J. Lopez-Abad, Lopez-Abad, J. +3
Mathematics · #46B42 #46B50 #47B07 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:46B42 #msc:46B50 #msc:47B07

paper · pdf · doi:10.48550/arxiv.1603.05573

13 pages

arxiv created 2016/03/17 · openalex publication_date 2016/03/17 · arxiv updated 2016/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We show that for every weakly compact subset K of C[0,1] with finite Cantor-Bendixson rank, there is a reflexive Banach lattice E and an operator T:E→ C[0,1] such that K⊆ T(B_E). On the other hand, we exhibit an example of a weakly compact set of C[0,1] homeomorphic to ω^ω+1 for which such T and E cannot exist. This answers a question of M. Talagrand in the 80's.

Citations

• Relative weak compactness of solid hulls in Banach lattices

Related

• Disjointly Weak Compactness in Banach Lattices
• Grothendieck's compactness principle for the absolute weak topology
• Weakly compactly generated Banach lattices
• Conic James' Compactness Theorem
• Banach Spaces Of The Type Of Tsirelson