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Abstract. In this note we study reducing subspaces for weighted composition operators defined on $L^2(\Sigma )$. Some necessary and sufficient conditions are given for such operators to have two types of reducing subspaces of the forms $L^2(\Sigma_A)$ and $L^2(\mathcal{A})$. This is basically discussed by using conditional expectation properties.
DOI: 10.14232/actasm-015-825-0
AMS Subject Classification
(1991): 47B37, 47B38
Keyword(s):
reducing subspace,
weighted composition operators,
conditional expectation
Received October 16, 2015. (Registered under 75/2015.)
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