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 2 / 3 . We also prove estimates for the K-divisibility constant of the two-dimensional version of the couple ( L 2 , 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.