Basic properties of unbounded weighted conditional type operators

In this paper we consider unbounded weighted conditional type (WCT) operators on Lp-space. We provide some conditions under which WCT Lp-spaces are densely defined. Specifically, obtain a dense subset of their domain. Moreover, get that operator is continuous if and only it every where A description polar decomposition, spectrum, spectral radius, normality hyponormality in context provided. Finally, apply results hyperexpansive to the Hilbert space L2(?). As consequence multiplication investigated.