Hypercyclic generalized shift operators (Q6160349)

In the paper under review, the authors give a characterization of hypercyclic generalized shift operators defined on the standard Hilbert module \(l^{2}(A)\), where \(A\) is a proper ideal of a unital commutative \(C^{*}\)-algebra. Also, they characterize some classes of hypercyclic operators defined on a \(C^{*}\)-algebra \(A\) corresponding to an isometric \(*\)-isomorphism \(\phi\) and a fixed element \(b \in A\). They construct an approximate identity for Segal algebras \(A_{\tau}\). They give some sufficient and necessary conditions for a new class of shift operators on \(A_{\tau}\) to be hypercyclic.