2014/06/04 by Nareen Sabih, Adem Kılıçman, Sabih, Nareen +1
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA
paper · pdf · doi:10.48550/arxiv.1406.0951
arxiv created 2014/06/04 · openalex publication_date 2014/06/04 · arxiv updated 2014/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we answer a question posed in the introduction of \citesub hyp positively, i.e, we show that if T is \mathcal M-hypercyclic operator with \mathcal M-hypercyclic vector x in a Hilbert space \mathcal H, then P(Orb(T,x)) is dense in the subspace \mathcal M where P is the orthogonal projection onto \mathcal M. Furthermore, we give some relations between \mathcal M⊥-hypercyclicity and the orthogonal projection onto \mathcal M⊥. We also give sufficient conditions for a bilateral weighted shift operators on a Hilbert space ℓ2(\mathbb Z) to be subspace-hypercyclic, cosequently, there exists an operator T such that both T and T^* are subspace-hypercyclic operators. Finally, we give an \mathcal M-hypercyclic criterion for an operator T in terms of its eigenvalues.