Cesàro means and convex-cyclic operators
IFZ Bensaid, F León-Saavedra… - Complex Analysis and …, 2020 - Springer
Complex Analysis and Operator Theory, 2020•Springer
We characterize when the Cesàro means of higher order for Banach spaces operators are
hypercyclic. This is a useful tool to prove that an operator is convex-cyclic and it provides a
large number of examples of convex-cyclic operators. A complex number λ λ is said to be an
extended eigenvalue of a bounded linear operator T if there exists a non-zero bounded
linear operator X such that TX= λ XT TX= λ XT. We will discover some necessary conditions
on the extended spectrum of an operator to be a convex-cyclic operator. These conditions …
hypercyclic. This is a useful tool to prove that an operator is convex-cyclic and it provides a
large number of examples of convex-cyclic operators. A complex number λ λ is said to be an
extended eigenvalue of a bounded linear operator T if there exists a non-zero bounded
linear operator X such that TX= λ XT TX= λ XT. We will discover some necessary conditions
on the extended spectrum of an operator to be a convex-cyclic operator. These conditions …
Abstract
We characterize when the Cesàro means of higher order for Banach spaces operators are hypercyclic. This is a useful tool to prove that an operator is convex-cyclic and it provides a large number of examples of convex-cyclic operators. A complex number is said to be an extended eigenvalue of a bounded linear operator T if there exists a non-zero bounded linear operator X such that . We will discover some necessary conditions on the extended spectrum of an operator to be a convex-cyclic operator. These conditions do not guarantee non-supercyclicity.
Springer