Weak commutation relations of unbounded operators: nonlinear extensions

Abstract

We continue our analysis of the consequences of the commutation relation $[S,T]=\Id$, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations.

Cited by in corpus (3)

• Non-self-adjoint hamiltonians defined by Riesz bases
• $\mathcal{D}$-deformed harmonic oscillators
• Everything is possible for the domain intersection dom T \cap dom T*