6533b850fe1ef96bd12a81b8
RESEARCH PRODUCT
On the regularity of the partial {$O\sp *$}-algebras generated by a closed symmetric operator
Jean-pierre AntoineCamillo TrapaniAtsushi Inouesubject
Discrete mathematicsPure mathematicsGeneral MathematicsHilbert spaceOperator theoryDifferential operatorAbstract theoryDomain (mathematical analysis)symbols.namesakeOperator algebraSimple (abstract algebra)symbolsMathematicsSymmetric operatordescription
Let be given a dense domain D in a Hilbert space and a closed symmetric operator T with domain containing D. Then the restriction of T to D generates (algebraically) two partial *-algebras of closable operators (called weak and strong), possibly nonabelian and nonassociative. We characterize them completely. In particular, we examine under what conditions they are regular, that is, consist of polynomials only, and standard. Simple differential operators provide concrete examples of all the pathologies allowed by the abstract theory.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1992-01-01 | Publications of the Research Institute for Mathematical Sciences |