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Journal of the London Mathematical Society Advance Access originally published online on March 11, 2009
Journal of the London Mathematical Society 2009 79(2):497-510; doi:10.1112/jlms/jdn081
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© 2009 London Mathematical Society

On orbit-reflexive operators

V. Müller and J. Vrsovsky

Mathematical Institute
Czech Academy of Sciences
Zitna 25
Prague 115 67
Czech Republic
vrsovsky@math.cas.cz

Let T be a bounded linear Banach space operator such that Formula . Then T is orbit-reflexive. In particular, every Banach space operator with a spectral radius different from 1 is orbit-reflexive. Better estimates are obtained for operators in Hilbert spaces. We also present a simple example of a nonorbit-reflexive Hilbert space operator and an example of a reflexive but nonorbit-reflexive operator (acting on {ell}1).

2000 Mathematics Subject Classification 47A15.

The research was supported by grant no. 201/06/0128 of GA CR and Institutional Research Plan AV 0Z 10190503.

Received November 23, 2007; revised October 30, 2008; published online March 11, 2009.


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