ON SUBSPACE BALANCED CONVEX-CYCLIC OPERATORS

Document Type : Original Article

Authors
Gholamreza Baseri 1
Ali Iloon Kashkooly 1
Hamid Rezaei 2
1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj-75914-74831, Iran.
2 Department of Mathematics, College of Sciences, Yasouj University, Yasouj75914-74831, Iran.
10.22034/maco.3.2.1
Abstract
 Let X be a separable Banach space and M be a subspace of X. A bounded Linear operator T on X is subspace balanced convex-cyclic for a subspace M, if there exists a vector x∈X such that the intersection of balanced convex hull of orb(T,x) with M is dense in M. We give an example of subspace balanced convex-cyclic operator that is not balanced convex-cyclic. Also we give an improvement of the Kitai-like criterion for subspace balanced convex-cyclicity and bring on with the Hahn-Banach characterization for
subspace balanced convex-cyclicity

Keywords

[1] D. Ahmed, M. Hama, J. Wozniak and K. Jwamer, On subspace convex-cyclic operators, Xiv : 1905.04781 [math.DS].
[2] M. Asadipour, Some notes on subspace convex-cyclicity, Journal of Mathematical Extension, Vol.16,no.5,(2022)(6) 1-9.
[3] Gh. Baseri, A. I. Kashkooli and H. Rezaei, On the balanced convex hull of operator’s orbit, Iran J Sci Technol Trans Sci, 46 (2022) 659-665.
[4] F. Bayart, E. Matheron, Dynamics of linear operators. Cambridge University press, New york, (2009).
[5] K. G. Grosse–Erdmann, A. Peris, Linear chaos universitext, Springer, (2011).
[6] B. F. Madore, R. A. Martinez–Avendano, Subspace hypercyclicity, J. Math. Anal. Appl. Vol 373, no. 2, PP. 502–511. (2011).
[7] H. Rezaei, On the convex hull generated by orbit of operators, Linear Algebra and its Applications, 438 (2013), 4190–4203.
Mathematical Analysis and Convex Optimization
Volume 3, Issue 2
December 2022
Pages 1-6