$Reducibility of $M_uC_\varphi$ on $L^2(\Sigma)

چکیده مقاله

In this note we study reducing subspaces for weighted composition
operators defined on L2(). Some necessary and sufficient conditions are given
for such operators to have two types of reducing subspaces of the forms L2(A)
and L2(A). This is basically discussed by using conditional expectation prop-
erties.