# Weak commutation relations of unbounded operators and applications

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.

Author: Fabio Bagarello; Atsushi Inoue; Camillo Trapani

Source: https://archive.org/