6533b83afe1ef96bd12a7ad9

RESEARCH PRODUCT

Weak commutation relations of unbounded operators and applications

Camillo TrapaniAtsushi InoueFabio Bagarello

subject

CommutatorPure mathematicsunbounded operatorsCommutation relationHilbert spaceMathematics - Operator AlgebrasFOS: Physical sciencesStatistical and Nonlinear PhysicsMathematical Physics (math-ph)symbols.namesakeSettore MAT/05 - Analisi MatematicaProduct (mathematics)Linear algebraFOS: MathematicssymbolsCommutationOperator Algebras (math.OA)Settore MAT/07 - Fisica MatematicaEigenvalues and eigenvectorsMathematical PhysicsMathematics

description

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. Some consequences on the existence of eigenvectors of two number-like operators are derived and the partial O*-algebra generated by $S,T$ is studied. Some applications are also considered.

yearjournalcountryeditionlanguage
2011-01-01
10.1063/1.3660682http://hdl.handle.net/10447/60630