التكرار في فضاء مؤثرات هلبرت-شميدت
محتوى المقالة الرئيسي
الملخص
في هذا البحث, تم برهان بانه اذا كانت شبه الزمرة-C0 فوضوية وزائدة او فائقة الاختلاط فان الضرب من جهة اليسار المرتبط بشبه الزمرة-C0 في فضاء مؤثرات هلبرت-شميدت متكرر اذا وفقط اذا كان مفرط الدوران. كذلك, تم بيان انه في ظل بعض الشروط يكون تكرار شبه الزمرة-C0 وتكرار الضرب لشبه الزمرة-C0 من جهة اليسار المرتبط بها في فضاء مؤثرات هلبرت-شميدت متكافئين. علاوة على ذلك, بعض الشروط الكافية للتكرار وزيادة الدوران للضرب من جهة اليسار لشبه الزمرة -C0 تم عرضها بالاعتماد على المجموعات الجزئية المتشعبة.
Received 07/04/2023
Revised 15/07/2023
Accepted 17/07/2023
Published Online First 20/10/2023
تفاصيل المقالة
هذا العمل مرخص بموجب Creative Commons Attribution 4.0 International License.
كيفية الاقتباس
المراجع
Grosse-Erdmann KG, Manguillot AP. Linear Chaos. London: Springer-Verlag; 2011. 388 p.
Moosapoor M. On the Recurrent C_0-semigroups, Their Existence, and Some Criteria. J Math. 2021; 2021: 1-7. https://doi.org/10.1155/2021/6756908.
Subrahmonian Moothathu TK. Orbital and Spectral Aspects of Hypercyclic Operators and Semigroups. Indag Math. 2019; 30: 1006-1022. https://doi.org/10.1016/j.indag.2019.07.007.
Jamil ZZ. On Hereditarily Codiskcyclic Operators. Baghdad Sci J. 2022; 19(2): 309-312. https://doi.org/10.21123/bsj.2022.19.2.0309.
Janfada M, Baghan AN. Hypercyclic Tuple C_0-semigroups of Operators. U P B Sci Bull Series A. 2019; 81: 103-110. https://www.scientificbulletin.upb.ro/rev_docs_arhiva/full844_195573.pdf.
Chong Y, Denghua Z. Chaotic Behavior of C_0-semigroup of Operators. Dyn Syst Appl. 2020; 29(2): 281-287. https://doi.org/10.46719/dsa20202926.
Bonilla A, Grosse-Erdmann KG, López-Martínez A, Peris A. Frequently Recurrent Operators. J Funct Anal. 2022; 283(12): 109713. https://doi.org/10.1016/j.jfa.2022.109713.
Moosapoor M, Nikoufar N. Some Properties and Citeria for Sub-chaotic C_0-semigroups. Jordan J Math Stat. 2022; 15(4B): 1065-1076. https://doi.org/10.47013/15.4.18.
Ahmed BA, Al-Janaby HF. Hypercyclictty and Countable Hypercyclicity for Adjoint of Operators. Baghdad Sci J. 2010; 7(1): 191-199. https://www.iasj.net/iasj/article/4013.
Desch W, Schappacher W. On Products of Hypercyclic Semigroups. Semigr Forum. 2005; 71: 301-311. https://doi.org/10.1007/s00233-005-0523-z.
Chan KC. Hypercyclicity of the Operator Algebra for a Separable Hilbert Space. J Oper Theory. 1999; 42: 231-244. https://www.jstor.org/stable/24715210.
Yousefi B, Rezaei H. Hypercyclicity on the Algebra of Hilbert-Schmidt Operators. Result Math. 2004; 46: 174-180. https://link.springer.com/article/10.1007/BF03322879
Yousefi B. Subspace Transitivity and Subspace Supercyclicity of Tuples of Operators in SOT and in the Norm of Hilbert-Schmidt Operators. J Math Ext 2017; 11: 71-81. https://ijmex.shiraz.iau.ir/index.php/ijmex/article/view/563/334.
Amouch M. Supercyclicity of Multiplication on Banach Ideal of Operators. Bol da Soc Parana de Mat. 2022; 40: 1-11. http://www.spm.uem.br/bspm/pdf/vol40/127.pdf.
Bes J, Peris A. Hereditarily Hypercyclic Operators. J Funct Anal. 1999; 167: 94-112. https://doi.org/10.1006/jfan.1999.3437.
Conejero J, Muller V, Peris A. Hypercyclic Behaviour of Operators in a Hypercyclic C_0-semigroup. J Funct Anal. 2007; 244: 342-348. https://doi.org/10.1016/j.jfa.2006.12.008.
Moosapoor M. Supermixing and Hypermixing of Strongly Continuous Semigroups and their Direct Sum. J Taibah Univ Sci. 2021; 15(1): 953-959. https://doi.org/10.1080/16583655.2021.2014092.