On the K-divisibility constant for some special finite-dimensional Banach couples

We prove new estimates of the K-divisibility constants for some special Banach couples. In particular, we prove that the K-divisibility constant for a couple of the form (U⊕V,U) where U and V are non-trivial Hilbert spaces equals . We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple (L2,L∞), proving in particular that this couple is not exactly K-divisible. There are also several auxiliary results, including some estimates for relative Calderón constants for finite-dimensional couples.