1-complemented subspaces of Banach spaces of universal disposition

2017/08/12 by Jesús M. F. Castillo, Castillo, Jesús M. F., Yolanda Moreno +1
Mathematics · #46B03 #46M40 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1708.03823

openalex publication_date 2017/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We first unify all notions of partial injectivity appearing in the literature ---(universal) separable injectivity, (universal) ℵ-injectivity --- in the notion of (α, β)-injectivity ((α, β)_λ-injectivity if the parameter λ has to be specified). Then, extend the notion of space of universal disposition to space of universal (α, β)-disposition. Finally, we characterize the 1-complemented subspaces of spaces of universal (α, β)-disposition as precisely the spaces (α, β)₁-injective.

Related

• Banach spaces of almost universal complemented disposition
• Universal disposition is not a 3-space property
• On separably injective Banach spaces and Corrigendum to "On separably injective Banach spaces" [Adv. Math. 234 (2013) 192--216]
• ℵ-injective Banach spaces and ℵ-projective compacta
• Complemented subspaces of J-sums of Banach spaces