Product of octahedra is badly approximated in the ${\ell }_{2,1}$-metric

Yu. V. Malykhin, K. S. Ryutin

We prove that the cartesian product of octahedra $B_{1,\infty }^{n,m}=B_1^n\times \dots \times B_1^n$ ($m$ octahedra) is badly approximated by half--dimensional subspaces in mixed--n…