BASIC PROPERTIES OF UNBOUNDED WEIGHTED CONDITIONAL TYPE OPERATORS

Abstract

In this paper we consider unbounded weighted conditional type

operators on the space Lp(), we give some conditions under which they are

densely dened and we obtain a dense subset of the domain. Also, we get

that a WCT operator is continuous if and only of it is every where dened.

A description of polar decomposition, spectrum, spectral radius, normality

and hyponormality in this context are provided. Finally, we investigate hy-

perexpansive WCT operators on the Hilbert space L2(). As a consequence

hyperexpansive multiplication operators are investigated.