2019/04/10 by Kadets, Vladimir, Zavarzina, Olesia
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1904.05392
We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces, namely the space whose unit sphere is a square (like ℓ_∞2 or ℓ12) and the space whose unit sphere is an equilateral hexagon. Finally, we address the question what are the spaces E = (\Rn, ‖⋅‖E) with absolute norm such that for every collection X1, …, Xn of GL-spaces their E-sum is a GL-space.