Banach spaces which always produce octahedral spaces of operators

2022/07/18 by Zoca, Abraham Rueda
#46B06 #46B20 #46B28 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2207.08717

Abstract

We characterise those Banach spaces X which satisfy that L(Y,X) is octahedral for every non-zero Banach space Y. They are those satisfying that, for every finite dimensional subspace Z, ℓ_∞ can be finitely-representable in a part of X kind of ℓ₁-orthogonal to Z. We also prove that L(Y,X) is octahedral for every Y if, and only if, L(ℓ_pⁿ,X) is octahedral for every n∈\mathbb N and 1

Related

• Octahedral norms in spaces of operators
• On octahedraliy and Müntz spaces
• L-orthogonality, octahedrality and Daugavet property in Banach spaces
• Interpolating hereditarily indecomposable Banach spaces
• Stability results of octahedrality in tensor product spaces