On interpolating sequences for Bloch type spaces

TL;DR

This paper extends the theory of interpolating sequences from $H^{ olinebreak ext{infty}}$ to Bloch type spaces, analyzing their properties and providing examples with arbitrarily small separation constants.

Contribution

It generalizes known interpolation results to Bloch type spaces and explores the relationship between different classes of interpolating operators.

Findings

Interpolation results extend from $H^{ olinebreak ext{infty}}$ to Bloch type spaces.

Examples of interpolating sequences with arbitrarily small separation constants.

Connections established between interpolating operators on different Bloch spaces.

Abstract

When we deal with $H^{\infty}$, it is 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 for Bloch type spaces $\mathcal{B}_{v}^\infty$ and study the connection between the interpolating operators on $\mathcal{B}_{v}^\infty$ and $\mathcal{B}_v^0$. Furthermore, for some particular weights $v$, we will provide examples of interpolating sequences for $\mathcal{B}_{v}^\infty$ whose constant of separation is as close to 0 as desired.