2021/12/07 by Thiago R. Alves, Alves, Thiago R., Pablo Turco +1
Mathematics · #15A03 #26A16 #46G20 #Advanced Banach Space Theory #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47B10 #Secondary 46G25
paper · pdf · doi:10.48550/arxiv.2112.03994
openalex publication_date 2021/12/07 · openalex created_date 2022/05/05 · openalex updated_date 2026/08/03
We provide quite sufficient conditions on the Banach spaces E and F in order to obtain the spaceability of the set of all linear operators from E into F which are q-compact but not p-compact. Also, under similar conditions over E, we prove that this set contains (up to the null operator) a copy of ℓs whenever F = ℓs. Finally, we give some applications of our previous results to show the spaceability of some sets formed by non-linear mappings (polynomial and Lipschitz) which are q-compact but not p-compact. The spaceability in the space of holomorphic mappings determined by p-compact sets is also considered.