## Seminari IMAC de Anàlisi: New approach on interpolating sequences for the Bloch space.

25/10/2021 | imac
Compartir

Compartir

Resum: When we deal with $$H^\infty$$ , the space of bounded analytic functions on the open unit disk, it is well-known that $$c_0$$ -interpolating sequences are interpolating and it is sufficient to interpolate idempotents of $$\ell^\infty$$ in order to interpolate the whole $$\ell^\infty$$. We will extend these results to the frame of interpolating sequences in the classical Bloch space B and we will provide new characterizations of interpolating sequences for B. For that, bearing in mind that $$B$$ is isomorphic but not isometric to the bidual of the little Bloch space $$B_0$$ , we will prove that given an interpolating sequence $$(z_n)_n$$ for $$B$$, the second adjoint of the interpolating operator which maps $$f$$ in $$B_0$$ to the sequence $$(f^\prime(z_ n ))(1-|z_n|^2 ))$$ can be perfectly identified with the corresponding interpolating operator from $$B$$ onto $$\ell^\infty$$. Furthermore, we will prove that interpolating sequences for $$H^\infty$$ are also interpolating for $$B$$. This yields us to provide examples of interpolating sequences which are $$\varepsilon$$-separated for the pseudohyperbolic distance for $$\varepsilon> 0$$ as small as we want such that $$\varepsilon$$ cannot be increased.