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

25/10/2021 | imac



Mario P.Maletzki  impartirà una xerrada al Seminari IMAC d'Anàlisi el proper 25 d'octubre de 2021, a la sala TI2328DS.
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.