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Properties of multi subspace-supercyclic operators and $C_0$-semigroups | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 01 مهر 1404 اصل مقاله (357.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.34509.5153 | ||
| نویسنده | ||
| Mansooreh Moosapoor* | ||
| Department of Mathematics Education, Farhangian University, Tehran, Iran | ||
| تاریخ دریافت: 31 خرداد 1403، تاریخ پذیرش: 26 بهمن 1403 | ||
| چکیده | ||
| In this paper, we describe multi-subspace-supercyclic operators and investigate them. We prove that any subspace-supercyclic operator and multi-supercyclic operator are multi-subspace-supercyclic. Also, we prove that an operator is multi-subspace-supercyclic if and only if any powers of it are multi-subspace-supercyclic. Furthermore, we define a subspace-supercyclic $C_{0}$-semigroup. We state that as a $C_{0}$-semigroup that contains a multi-subspace-supercyclic operator, it is multi-subspace-supercyclic. | ||
| کلیدواژهها | ||
| Subspace-supercyclic operators؛ Multi subspace-supercyclic operators؛ Subspace-supercyclic C0-semigroups؛ Multi subspace-supercyclic C0-semigroups | ||
| مراجع | ||
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[1] A. Augusto and L. Pellegrini, On the existence of subspace-hypercyclic operators and a new criteria for subspace-hypercyclicity, Adv. Oper. Theory 5 (2020), no. 4, 1814–1824. [2] N. Bamerni, V. Kadets and A. Kilicman, Hypercyclic operators are subspace-hypercyclic, J. Math. Anal. Appl. 435 (2016), no. 2, 1812–1815. [3] M. El Berrag and A. Tajmouati, On subspace-supercyclic semigroup, Commun. Korean Math. Soc. 33 (2018), 157–164. [4] K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Springer, 2011. [5] A. Kumar and S. Srivastava, Supercyclicity criteria for C0-semigroups, Adv. Oper. Theory 5 (2020), no. 4, 1646–1666. [6] Y.X. Liang and Z.H. Zhou, Supercyclic translation C0-semigroup on complex sectors. Dyn. Syst. 36 (2016), no. 1, 361–370. [7] B.F. Madore and R.A. Martiınez-Avendano, Subspace hypercyclicity, J. Math. Anal. Appl. 373 (2011), 502–511. [8] M. Moosapoor, Some criteria for subspace-hypercyclicity of C0-semigroups, Aust. J. Math. Anal. Appl. 18 (2021), no. 1, Article 12, 8 pp. [9] M. Moosapoor, On subspace-supercyclic operators, Aust. J. Math. Anal. Appl. 17 (2020), Art. 4, 8 pp. [10] A. Peris, Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), 779–786. [11] L. Zhang and Z.H. Zhou, Notes about subspace-supercyclic operators, Ann. Funct. Anal. 6 (2015), 60–68 [12] X.F. Zhao, Y.L. Shu, and Y.H. Zhou, Subspace-supercyclicity and common subspace-supercyclic vectors, J. East China Norm. Univ. Natural Sci. 1 (2012), 106. | ||
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