2023/02/22 by Cleon S. Barroso, Barroso, Cleon S.
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2302.11287
openalex publication_date 2023/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper brings new results on the FPP in Banach spaces X with a Schauder basis. We first deal with the problem of whether there is a Banach space isomorphic to \co having the FPP. We show that the answer is negative if X contains a pre-monotone basic sequence equivalent to the unit basis of \co. We then study sufficient conditions to ensure the existence of such sequences. Interesting results are obtained, including the case when X has a 1-suppression unconditional basis and its unit ball fails the PCP. With regarding the weak-FPP, we establish two fixed-point results. First, we show that under certain conditions this property is invariant under Banach-Mazur distance one. Next, it is shown that when the basis is either 1-suppression unconditional or 1-spreading then X has the weak-FPP provided that a Rosenthal's type property on block basis is verified.