K-divisibility constants for some special couples

Details K-divisibility constants for some special couples K-divisibility constants for some special couples

2005-12-12

arxiv.org/abs/math/0512234v2

Mathematics

Functional Analysis

Scientific paper

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 $(U\oplus V, U)$ where $U$ and $V$ are non-trivial Hilbert spaces equals $2/\sqrt{3}$. We also prove estimates for the $K$-divisibility constant of the two-dimensional version of the couple $(L_2,L_\infty)$, proving in particular that this couple is not exactly $K$-divisible. There are also several auxiliary results, including some estimates for relative Calder\'on constants for finite dimensional couples.

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