论文标题
FOCK代表自由卷积权力
Fock representation of free convolution powers
论文作者
论文摘要
令$ b $为具有状态$ ϕ $的星空代数，$ t> 0 $。通过FOCK空间构造，我们定义了两个状态$φ_T$和$ψ_T$在张量代数$ t（b，ϕ）$上，使自然地图$（b，ϕ）\ rightRarow（t（b，ϕ），φ_t，ψ_t，ψ_t）$，参数自由独立独立的独立独立的独立独立性的独立共同行为独立的独立独立性的独立范围。该构造为任何关节分布的$（1+t）$'th自由卷积功率提供了新的操作员。我们还计算出出现的几个冯·诺伊曼代数。
Let $B$ be a star-algebra with a state $ϕ$, and $t > 0$. Through a Fock space construction, we define two states $Φ_t$ and $Ψ_t$ on the tensor algebra $T(B, ϕ)$ such that under the natural map $(B, ϕ) \rightarrow (T(B, ϕ), Φ_t, Ψ_t)$, 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.
