2000 character limit reached
On subspaces of $\ell_\infty$ and extreme contraction in $\mathbb{L}(\mathbb{X}, \ell_{\infty}^n)$ (2208.10184v1)
Published 22 Aug 2022 in math.FA
Abstract: We investigate different possiblities of subspaces of the space $\ell_{\infty}$ in terms of whether the subspaces are polyhedral or not. We further study finite-dimensional subspaces of $\ell_{\infty}$ which are of the form $\ell_\inftyn$ form some $ n \geq 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 $\mathbb{L}(\mathbb{X}, \ell_{\infty}n),$ where $\mathbb{X}$ is a finite-dimensional polyhedral space.