The Bender-Dunne basis operators as Hilbert space operators

The Bender-Dunne basis operators, $$\mathsf{T}${-m,n}=2^{-n}\sum{k=0}^n {n \choose k} $\mathsf{q}$^k $\mathsf{p}$^{-m} $\mathsf{q}$^{n-k}$where$$\mathsf{q}$$and$$\mathsf{p}$$ are the position and momentum operators respectively, are formal integral operators in position representation in the entire real line $\mathbb{R}$ for positive integers $n$ and $m$. We show, by explicit construction of a dense domain, that the operators ${\mathsf{T}}_{-m,n}$'s are densely defined operators in the Hilbert space $L^2(\mathbb{R})$.