Fock representation of free convolution powers - Texas A&M University (TAMU) Scholar

Let $B$ be a star-algebra with a state $phi$, and $t > 0$. Through a Fock space construction, we define two states $Phi_t$ and $Psi_t$ on the tensor algebra $T(B, phi)$ such that under the natural map $(B, phi)
ightarrow (T(B, phi), Phi_t, Psi_t)$, free independence of arguments leads to free independence, while Boolean independence of centered arguments leads to conditionally free independence. The construction gives a new operator realization of the $(1+t)$'th free convolution power of any joint (star) distribution. We also compute several von Neumann algebras which arise.

Fock representation of free convolution powers Institutional Repository Document