2023/04/19 by Gustavo Araújo, Anderson Barbosa, Araújo, Gustavo +5
Mathematics · #15A03 #46B87 #46E30 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2304.09581
openalex publication_date 2023/04/19 · openalex created_date 2023/04/22 · openalex updated_date 2026/07/28
In this note we prove that, for p>0, Lp[0,1]\smallsetminus\bigcupq∈(p,∞)Lq[0,1] is (α,\mathfrakc)-spaceable if, and only if, α<ℵ0. Such a problem first appears in [V. Fávaro, D. Pellegrino, D. Tomaz, Bull. Braz. Math. Soc. 51 (2020) 27-46], where the authors get the (1,\mathfrakc)-spaceability of Lp[0,1]\smallsetminus\bigcupq∈(p,∞)Lq[0,1] for p>0. The definitive answer to this problem continued to be sought by other authors, and some partial answers were obtained. The veracity of this result was expected, as a similar result is known for sequence spaces.