Abstract
In this paper, we characterize nontrivially essentially self-adjoint weighted composition operators on the Hardy space
and the weighted Bergman spaces
, when
is not an automorphism and
is continuous at
. Moreover, we show that weighted composition operators
on
and
are not nontrivially essentially self-adjoint, whenever
and
for
.
Acknowledgments
The authors appreciate Prof. B.D. MacCluer for her attention and development of Proposition 3.1.