Over time the concept of hypercyclicity has been explored in different manners and contexts, gaining new forms applications. In particular when space an adjacent structure, we can always look for sets hypercyclic vectors compatible with that framework. this paper deal operators acting on Fréchet sequence algebras give criteria existence common disjoint algebras.

Abstract In this survey we report about recent work on weighted Banach spaces of analytic functions the unit disc and whole complex plane defined with sup-norms operators between them. Results solid hull core these distance formulas are reviewed. Differentiation integration operators, Cesàro Volterra composition superposition Toeplitz analyzed. Boundedness, compactness, spectrum, hypercyclicity...