Induced and reduced unbounded operator algebras

TL;DR

This paper investigates how induction and reduction processes affect unbounded operator algebras, specifically partial GW*-algebras, providing conditions under which these properties are preserved.

Contribution

It introduces conditions ensuring that induced and reduced unbounded operator algebras remain partial GW*-algebras, advancing understanding of their structural stability.

Findings

Sufficient conditions for induced spaces to be partial GW*-algebras

Sufficient conditions for reduced spaces to be partial GW*-algebras

Analysis of induction and reduction processes in unbounded operator algebras

Abstract

The induction and reduction precesses of an O*-vector space $\M$ obtained by means of a projection taken, respectively, in $\M$ itself or in its weak bounded commutant $\M'_\w$ are studied. In the case where $\M$ is a partial GW*-algebra, sufficient conditions are given for the induced and the reduced spaces to be partial GW*-algebras again.