Chaotic extensions of operators on Hilbert subspaces



If M is a closed subspace of a separable, infinite dimensional Hilbert space H with dim (H/M) = ∞, we show that every bounded linear operator A: MM can be extended to a chaotic operator T: HH that satisfies the hypercyclicity criterion in the strongest possible sense.


Chaotic extension Hypercyclic extension Invariant subspace Infinite codimension 

Mathematics Subject Classification (2000)

47A16 46A22 47A15 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA

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