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Disjoint hypercyclic and supercyclic composition operators

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  1. Tez No: 400096
  2. Yazar: ÖZGÜR MARTİN
  3. Danışmanlar: JUAN BÉS
  4. Tez Türü: Doktora
  5. Konular: Matematik, Mathematics
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 2010
  8. Dil: İngilizce
  9. Üniversite: Bowlıng Green State Unıversıty
  10. Enstitü: Yurtdışı Enstitü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: Belirtilmemiş.

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Özet (Çeviri)

Finitely many hypercyclic (respectively, supercyclic) operators acting on a common topologicalvector space are called disjoint if their direct sum has a hypercyclic (respectively,supercyclic) vector on the diagonal. In this dissertation, we characterize disjointness amonghypercyclic and supercyclic linear fractional composition operators on the Hardy space,complementing a celebrated characterization of the cyclic behavior of such operators due toBourdon and Shapiro [P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for compositionoperators, Mem. Amer. Math. Soc. 125 (1997)].Finitely many hypercyclic (respectively, supercyclic) operators acting on a common topologicalvector space are called disjoint if their direct sum has a hypercyclic (respectively,supercyclic) vector on the diagonal. In this dissertation, we characterize disjointness amonghypercyclic and supercyclic linear fractional composition operators on the Hardy space,complementing a celebrated characterization of the cyclic behavior of such operators due toBourdon and Shapiro [P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for compositionoperators, Mem. Amer. Math. Soc. 125 (1997)].We use our characterization to answer a question by Bernal [L. Bernal-Gonzalez, Disjointhypercyclic operators, Studia Math. 182 Vol 2 (2007) 113{131, Problem 3], whether nitelymany hypercyclic composition operators on H(D) generated by non-elliptic automorphismsare disjoint. We also apply our characterization to provide N 2 invertible hypercyclicoperators that are disjoint and so that their inverses are not disjoint supercyclic, solving aproblem by Bes and Peris [J. Bes and A. Peris, Disjointness in hypercyclicity, J. Math. Anal.Appl. 336 (2007) 297{315, Problem 3].We also provide characterizations for disjointness of nitely many hypercyclic (respectively,supercyclic) sequences of composition operators with automorphic symbols of anysimply connected domain. We show that finitely many sequences of composition operatorsinduced by automorphic symbols are disjoint hypercyclic if and only if they are disjointsupercyclic, complementing and improving recent work by Bernal, Bonilla, and Calder on[L. Bernal-Gonzalez, A. Bonilla and M. C. Calder on-Moreno, Compositional hypercyclicityequals supercyclicity, Houston Journal of Mathematics 3 No 2 (2007) 581{591].Finally, we characterize disjointness among powers of supercyclic shift operators on `pspaces (1 p < 1), complementing the study of the hypercyclic case by Bes and Peris.

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