Peripheral Poisson Boundary on Full Fock space

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 $\mathit{\text{peripheral}}\mathit{\text{Poisson}}\mathit{\text{boundary}}$ 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 $B(\text{mcal}F(H))$ and explore its behavior with respect to the Poisson boundary.