2024/06/17 by Mainak Ghosh, Ghosh, Mainak
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Algebraic structures and combinatorial models #Nonlinear Photonic Systems
paper · pdf · doi:10.48550/arxiv.2406.11167
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 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.