AbstractFor holomorphic pairs of symbols $$(u, \psi )$$
(
u
,
ψ
)
, we study various structures of the weighted composition operator $$ W_{(u,\psi )} f= u \cdot f(\psi )$$
W
(
u
,
ψ
)
f
=
u
·
f
(
ψ
)
defined on the Fock spaces $$\mathcal {F}_p$$
F
p
. We have identified operators $$W_{(u,\psi )}$$
W
(
u
,
ψ
)
that have power-bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values |u(0)| and $$|u(\frac{b}{1-a})|$$
|
u
(
b
1
-
a
)
|
, where a and b are coefficients from linear expansion of the symbol $$\psi $$
ψ
. The spectrum of the operators is also determined and applied further to prove results about uniform mean ergodicity.
A Remark on Isometries of Absolutely Continuous Spaces
