Spectral radius algebras of wce operators

TL;DR

This paper explores spectral radius algebras associated with weighted conditional expectation operators on Hilbert spaces, revealing their structure, invariance under transformations, and relationships with rank-one operators.

Contribution

It characterizes spectral radius algebras for weighted conditional expectation operators, showing their invariance under Aluthge transformation and identifying related ideals.

Findings

Spectral radius algebras of weighted conditional expectation operators are characterized.

Spectral radius algebras of an operator and its Aluthge transform are equal.

An ideal related to rank-one operators within the spectral radius algebra is identified.

Abstract

In this paper, we investigate the spectral radius al- gebras related to the weighted conditional expectation operators on the Hilbert spaces L2(F). We give a large classes of operators on L2(F) that have the same spectral radius algebra. As a con- sequence we get that the spectral radius algebras of a weighted conditional expectation operator and its Aluthge transformation are equal. Also, we obtain an ideal of the spectral radius algebra related to the rank one operators on the Hilbert space H. Finally we get that the operator T majorizes all closed range elements of the spectral radius algebra of T, when T is a weighted condi- tional expectation operator on L2(F) or a rank one operator on the arbitrary Hilbert space H.