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Background: For any fixed $t> 0$, the $K$-functional defines a norm on the space $\ell_1+\ell_2$: $$ \lVert a\rVert_{K(t)} = \inf\{\lVert a'\rVert_1+ t\lVert a''\rVert_2 : a'\in\ell_1,\ a''\in\...

Let $\rho:[0,+\infty)^{\mathbb{N}}\to[0,+\infty] $ satisfy the following properties: $\rho(\lambda u)=\lambda\rho( u)$, for every $u\in [0,+\infty)^{\mathbb{N}}$ and $\lambda\ge 0$; $\rho(u+v)\le \...