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Abstract. We investigate the link of cyclic behavior between a bounded operator and its Generalized Aluthge transforms. As an application, we characterize $\omega $-hyponormal operators for which the adjoint is hypercyclic or supercylic in terms of analytic spectral spaces. This extends a recent result of N. Feldman, V. G. Miller and T. L. Miller given for hyponormal operators.
AMS Subject Classification
(1991): 47A10, 47A11, 47B20
Keyword(s):
hypercyclic,
supercyclic,
\omega,
-hyponormal,
generalized Aluthge transforms
Received March 28, 2008, and in revised form September 17, 2008. (Registered under 6074/2009.)
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