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Abstract
In this paper, we consider the self-commutator of an invertible weighted composition operator on the Hardy space
where
is continuous on
. We show that both the self-commutator
and the anti-self-commutator
are expressed as compact perturbations of Toeplitz operators. Moreover, we give an alternative proof for the result in [Citation2] that
is unitary exactly when
is an automorphism of
and
where
,
is the reproducing kernel at
for
, and
is a constant with
. We next show that when
for all
, the weighted composition operator
is normal if and only if the composition operator
is unitary and
is constant on
. We also provide some spectral properties of
and
.
Acknowledgments
The authors wish to thank the referee for a careful reading and valuable comments for the original draft. This work was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) grant funded by the Korea government(MEST)(2012-0000939).
Notes
This version has been corrected. Please see Erratum (http://dx.doi.org/10.1080/17476933.2013.810458)