Bulletin of the
Korean Mathematical Society BKMS

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

Keywords: weighted composition operator, conditional expectation, multiplication operator, Fredholm operator

MSC numbers: Primary 47B20; Secondary 47B38