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