Some unbounded commutants of a set of operators on a partial inner product space

Abstract

This paper continues our systematic study of unbounded commutants within the framework of operators on a partial inner product (PIP) space. The most general commutant of a set of operators on a PIP space is considered and its behavior with respect to a topology finer than the weak and quasiweak *-topologies used in previous investigations is studied. The relationship between a bicommutant introduced by Shabani and a bicommutant introduced by Araki and Jurzak for closed Op*-algebras satisfying some countability conditions is given.