Local Blaschke--Kakutani ellipsoid characterization and Banach's isometric subspaces problem

Sergei Ivanov, Daniil Mamaev, Anya Nordskova

We prove the following local version of Blaschke--Kakutani's characterization of ellipsoids: Let $V$ be a finite-dimensional real vector space, $B\subset V$ a convex body with 0 in…