Abstract
In this paper we will consider the weighted composition operator <TEX>$W=uC_{\varphi}$</TEX> between two different <TEX>$L^p(X,\;\Sigma,\;\mu)$</TEX> spaces, generated by measurable and non-singular transformations <TEX>$\varphi$</TEX> from X into itself and measurable functions u on X. We characterize the functions u and transformations <TEX>$\varphi$</TEX> that induce weighted composition operators between <TEX>$L^p-spaces$</TEX> by using some properties of conditional expectation operator, pair <TEX>$(u,\;\varphi)$</TEX> and the measure space <TEX>$(X,\;\Sigma,\;\mu)$</TEX>. Also, Fredholmness of these type operators will be investigated.
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