Unbounded Weighted Conditional Expectation Operators

摘要

In this note some basic properties of unbounded weighted conditional expectation operators are investigated. A description of polar decomposition, spectrum, normality, quasi-normality and self-adjointness in this context are provided. Also, we give some necessary and sufficient conditions for EMu to leave invariant its domain. Finally, some examples are provided to illustrate concrete application of the main results of the paper.