Semigroups of operators on quotient spaces of \(H^ 2\)
Let \(\phi\) be an inner function on the unit disc \(\mathbb{D}=\{z\in\mathbb{C}: | z| <1\}\); \(S\) be standard unilateral shift on \(H^ 2(\mathbb{D})\), i.e. \(S: f(z)\to zf(z)\); \(S_ \phi\) is the compression of \(S\) onto \(H^ 2/\phi H^ 2\); \(A(\phi)\) is the commutant of \(S_ \phi\). A sufficient condition for a fixed operator in \(A(\phi)\) to be embeddable in a \(C_ 0\)-semigroup of operators in \(A(\phi)\) is given. If this semigroup consists of contraction operators, then this condition is necessary.
scientific article; zbMATH DE number 91587