$J$-Class Semigroup Operators

Abstract

A C0-semigroup T = (Tt) t≥0 on an infinite-dimensional separable complex Banach space X is called subspace-hypercyclic for a subspace M, if Orb(T , x) M is dense in M for a vector x ∈ M . In this paper, we localize the notion of M-extended semigroup(resp.M-extended semigroup mixing) limit set of x under T and We give sufficient conditions of being M -hypercyclic for this semigroup. Then by this result, we prove that (T −1 t ) t≥0 is a M -hypercyclic. This result is an answer of the question of B. F. Madore and R. A. Martnez-Avendano for C0-semigroup.

On Cesaro-Hypercyclic Operators

“…A bounded linear operator T ∈ B(H ) is called supercyclic if there is some vector x ∈ H such that the projective orbit C.Orb(T, x) = {λT n x : λ ∈ C, n ∈ N} is dense in X. Such a vector x is said supercyclic for T. Refer to ( [1], [9], [4], [15]) for more informations about hypercyclicity and supercyclicity.…”

Some Results on Subspace Cesaro-Hypercyclic Operators

“…A bounded linear operator T ∈ B(H ) is called supercyclic if there is some vector x ∈ H such that the projective orbit C.Orb(T, x) = {λT n x : λ ∈ C, n ∈ N} is dense in X. Such a vector x is said supercyclic for T. Refer to ( [1], [8], [4], [19]) for more informations about hypercyclicity and supercyclicity.…”