Weak commutation relations of unbounded operators and applications

Abstract

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.

In press in Journal of Mathematical Physics

References in corpus (2)

• Examples of Pseudo-bosons in quantum mechanics
• Pseudo-bosons, Riesz bases and coherent states

Cited by in corpus (3)

• Non-self-adjoint hamiltonians defined by Riesz bases
• $\mathcal{D}$-deformed harmonic oscillators
• Weak commutation relations of unbounded operators: nonlinear extensions