Decompositions of Weighted Conditional Expectation Type Operators

TL;DR

This paper explores the mathematical properties of weighted conditional expectation operators, focusing on their boundedness, polar, and spectral decompositions within the L^2 space.

Contribution

It provides new insights into the structure and spectral analysis of weighted conditional expectation operators, extending existing theoretical frameworks.

Findings

Characterization of boundedness conditions

Derivation of polar decomposition formulas

Spectral decomposition results for these operators

Abstract

In this paper we investigate boundedness, polar decomposition and spectral decomposition of weighted conditional expectation type operators on L^2(\Sigma).