Mixing operators on spaces with weak topology

• Autorzy: Shkarin S.
• Języki publikacji: EN

Abstrakty

EN

We prove that a continuous linear operator T on a topological vector space X with weak topology is mixing if and only if the dual operator T′ has no finite dimensional invariant subspaces. This result implies the characterization of hypercyclic operators on the space ω due to Herzog and Lemmert and implies the result of Bayart and Matheron, who proved that for any hypercyclic operator T on ω, T⊕T is also hypercyclic.

Słowa kluczowe

EN

hypercyclic operators; transitive operators; mixing operators; weak topology

PL

operatory hipercykliczne; topologia

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 1
• Strony: 143--150
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Shkarin S.

• Queens's University Belfast, Department of Pure Mathematics, University Road, Belfast, BT7 1NN, UK

Bibliografia

• [1] F. Bayart, E. Matheron, Hypercyclic operators failing the hypercyclicity criterion on classical Banach spaces, J. Funct. Anal. 250 (2007), 426–441.
• [2] F. Bayart, E. Matheron, Dynamics of Linear Operators, Cambridge University Press, 2009.
• [3] J. Bés, J. Conejero, Hypercyclic subspaces in omega, J. Math. Anal. Appl. 316 (2006), 16–23.
• [4] K. Chan, R. Sanders, A weakly hypercyclic operator that is not norm hypercyclic, J. Operator Theory 52 (2004), 39–59.
• [5] G. Herzog, R. Lemmert, Über Endomorphismen mit dichten Bahnen, Math. Z. 213 (1993), 473–477.
• [6] H. Petersson, Hypercyclicity in omega, Proc. Amer. Math. Soc. 135 (2007), 1145–1149.
• [7] S. Shkarin, Non-sequential weak supercyclicity and hypercyclicity, J. Funct. Anal. 242 (2007), 37–77.
• [8] J. Wengenroth, Hypercyclic operators on non-locally convex spaces, Proc. Amer. Math. Soc. 131 (2003), 1759–1761.