Sums of weighted composition operators on COP. (English) Zbl 1264.47027
Let \(B_0\) be the little Bloch space on the unit disk and \(\text{COP}=B_0\cap H^\infty\). Note that COP coincides with the subspace of all bounded analytic functions whose Gelfand transform is constant on every non-trivial Gleason part within the corona \(M(H^\infty)\setminus \mathbb D\) of the maximal ideal space \(M(H^\infty)\) of \(H^\infty\). The authors describe those \(n\)-tuples of functions \(\phi_j, u_j\in A(\mathbb D)\) with \(\|\phi_j\|_\infty\leq 1\) for which the sum \(\sum_{j=1}^n u_j C_{\phi_j}\) of weighted composition operators maps COP into \(A(\mathbb D)\).
Reviewer: Raymond Mortini (Metz)
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