Hypercyclic Conjugate Operators |
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Authors: | Henrik Petersson |
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Institution: | 1.School of Mathematical Sciences,Chalmers/G?teborg University,G?teborg,Sweden |
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Abstract: | We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 47A16 47B49 47A58 47L10 47B10 |
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