On M-hypercyclic semigroup

Abstract

In this work we introduce and study the M-Hypercyclicity of C 0-semigroup T = (T t) t≥0 on an infinite-dimensional separable complex Banach space X. We give sufficient conditions of being M-hypercyclic for this semigroup. Moreover, some proprieties and analogous result for the notion of M-Transitive are also obtained.

$J$-Class Semigroup Operators

“…Definition 2.1. [17] Let T = (T t ) t≥0 be a C 0 -semigroup and M be a nonzero subspace of X. We say that T is M −hypercyclic if there exists a vector…”

“…Recently, in 2015 Abdelaziz Tajmouati , Abdeslam El Bakkali and Ahmed Toukmati introduced and studied the M -Hypercyclicity of C 0 -semigroup T = (T t ) t≥0 on an infinite-dimensional separable complex Banach space X and gave sufficient conditions of being M -hypercyclic for this semigroup. Moreover, some proprieties and analogous results for the notion of M -transitive, see [17].…”

On the M-hypercyclicity of cosine function on Banach spaces

“…The M -hypercyclicity of C 0 -semigroups are crucial for the investigation of hypercyclicity of C 0 -semigroups; we refer to [15], [17], [18] for some references. The motivation for the study of M -hypercyclicity of cosine operator function is inspired by the work of A. Bonilla and P.J.…”

The $M$-Hypercyclicity Criterion of $C_{0}$-Semigroups

“…In [20] we investigated and studied the hyperyclicity in non trivial subspace for the C 0 -semigroups. Let T = (T t ) t≥0 be a C 0 -semigroup on separable Banach space X, T is called M -hypercyclic for M a subspace of X if there is a vector…”

“…An other hand we proved that if (T t ) t≥0 is M -hypercyclic then for every λ ∈ C and t > 0 we have ker(T * t − λI) ⊂ M ⊥ (T * t the adjoint of T t ), and we were giving a condition for a C 0 -semigroup to be M -hypercyclic. In [21] we showed that in every separable infinite dimensional Banach space there is a C 0 -semigroups M -hypercyclic for some subspace M , and any hypercyclic C 0 -semigroups is Mhypercyclic for some subspace M but the converse is not true in general (see also [15]). …”