Journal of the
Korean Mathematical Society JKMS

In this paper we will consider the weighted composition operators $W=uC_\tau$ between $L^p(X,\Sigma, \mu)$ spaces and Orlicz spaces $L^\varphi(X,\Sigma,\mu)$, generated by measurable and non-singular transformations $\tau$ from $X$ into itself and measurable functions $u$ on $X$. We characterize the functions $u$ and transformations $\tau$ that induce weighted composition operators between $L^p$-spaces by using some properties of conditional expectation operator, pair ($u$, $\tau$) and the measure space $(X,\Sigma,\mu)$. Also, some other properties of these types of operators will be investigated.

Keywords: weighted composition operator, conditional expectation, Fredholm operator, Orlicz space

MSC numbers: Primary 47B20, 47B33; Secondary 47B38, 46E30