A characterization of positive normal functionals on the full operator algebra

TL;DR

This paper develops criteria to determine when positive functionals on the full operator algebra are normal, utilizing Krein--von Neumann extension theory, and characterizes those with normal extensions from finite rank operators.

Contribution

It introduces new criteria for normality of positive functionals and characterizes extensions from finite rank operators using Krein--von Neumann theory.

Findings

Provided simple criteria for normality of positive functionals

Characterized positive functionals with normal extensions from finite rank operators

Applied Krein--von Neumann extension theory to operator algebras

Abstract

Using the recent theory of Krein--von Neumann extensions for positive functionals we present several simple criteria to decide whether a given positive functional on the full operator algebra is normal. We also characterize those functionals defined on the left ideal of finite rank operators that have a normal extension.