Partial *-algebras of closed linear operators in Hilbert space (Q1086822)

The authors study partial *-algebras of (unbounded) closed operators with a joint (not invariant in general) dense domain in a Hilbert space. The algebraic operations are defined only for some pairs of operators. The authors consider two types of extensions of the set of closable operators for a given domain D. These are the set of so called D-minimal operators and the set of D-maximal operators, in which the appropriate partial algebraic structure can be defined. Also topologies have been found with respect to which the algebraic operations are continuous. Finally, the notion of a commutant in the presented approach is studied.