Unbounded weighted conditional type operators on L^p spaces

TL;DR

This paper studies unbounded weighted conditional type operators on L^p spaces, providing conditions for their domain, continuity, and spectral properties, and explores hyperexpansiveness in the Hilbert space context.

Contribution

It offers new insights into the domain, continuity, spectral decomposition, and hyperexpansiveness of unbounded weighted conditional type operators on L^p spaces.

Findings

Conditions for dense domain of WCT operators

Characterization of continuity as everywhere defined

Analysis of hyperexpansive operators on L^2

Abstract

In this paper we consider unbounded weighted conditional type operators on the space Lp, we give some conditions under which they are densely defined 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 defined. A description of polar decomposition, spectrum and spectral radius in this context are provided. Finally, we investigate hyperexpansive WCT operators on the Hilbert space L2. As a consequence hyperexpansive multiplication operators are investigated.