  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 $L^2(\mathbb{R})$.
