Extreme contractions on finite-dimensional Banach spaces
Tom 172 / 2023
Streszczenie
We study extreme contractions in the setting of finite-dimensional polyhedral Banach spaces. Motivated by the famous Krein–Milman Theorem, we prove that a rank linear operator of unit norm between such spaces can be expressed as a convex combination of rank 1 extreme contractions whenever the domain is two-dimensional. We establish that the same result holds true in the space of all linear operators from \ell _{\infty }^n(\mathbb C) to \ell _1^n (\mathbb C). Furthermore, we present a geometric characterization of extreme contractions between finite-dimensional polyhedral Banach spaces.