K-divisibility constants for some special couples

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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 (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.