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.
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