  The operator space generated by peripheral eigenvectors of a unital normal
completely positive map $P$ on a von Neumann algebra has a C*-algebra
structure. This C*-algebra is known as the \textit{peripheral Poisson boundary}
of $P$. For a separable Hilbert space $H$, consider the full fock space defined
over $H$. In this paper, we study the peripheral Poisson boundary of the
completely positive map, induced by left creation operators of the basis
vectors of $H$, on $B(\mcal F(H))$ and explore its behavior with respect to the
Poisson boundary.
