On subspaces of ℓ_∞ and extreme contraction in \mathbbL(\mathbbX, ℓ_∞ⁿ)

2022/08/22 by Sohel, Shamim, Sain, Debmalya, Paul, Kallol
#46B20 #47L05 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2208.10184

Abstract

We investigate different possiblities of subspaces of the space ℓ_∞ in terms of whether the subspaces are polyhedral or not. We further study finite-dimensional subspaces of ℓ_∞ which are of the form ℓ_∞ⁿ form some n ≥ 2. As an application of the results we compute the number of extreme contractions for a class of the space of bounded linear operators. In particular we find the number of extreme contractions of \mathbbL(\mathbbX, ℓ_∞ⁿ), where \mathbbX is a finite-dimensional polyhedral space.

Related

• Extreme contractions on finite-dimensional polygonal Banach spaces-II
• Polylog dimensional subspaces of ℓ_∞^N
• When is a subspace of ℓ_∞^N isometrically isomorphic to ℓ_∞ⁿ?
• Does a typical \ℓ_p ,- ,space contraction have a non-trivial\n invariant subspace?
• A Geometric Characterization of Extremal Sets in ell_p Spaces