A non-selfadjoint Russo-Dye theorem
We prove a Russo-Dye theorem for an infinite multiplicity nest algebra \(\text{Alg } {\mathcal N}\): if \(A\) is an operator in \(\text{Alg } {\mathcal N}\) so that \(|A|< (n-1)/ (n+1)\), then there exist \(16n (n+1)\) unitary operators from \(\text{Alg } {\mathcal N}\) whose mean is equal to \(A\). A similar result is also valid for the algebra of the Cantor nest \({\mathcal N} (\mathbb{Q})\) and other operator algebras. Our results locate the first classes of non-selfadjoint operator algebras for which a Russo-Dye type theorem is valid.
scientific article; zbMATH DE number 838436
scientific article