论文标题
在$ Q $ -Gaussian W $^\ ast $ -Algebras的同构中
On the isomorphism class of $q$-Gaussian W$^\ast$-algebras for infinite variables
论文作者
论文摘要
令$ m_q（h _ {\ mathbb {r}}）$为$ q $ -gaussian von neumann algebra，与可分离的无限尺寸真实的Hilbert Space $ h _ {\ Mathbb {r}} $ -1 <q <q <q <q <1 $ $。我们表明$ M_Q（H _ {\ Mathbb {r}}）\ not \ simeq M_0（H _ {\ Mathbb {r}}）$ for $ -1 <q \ not = 0 <1 $。该结果的C $^\ AST $ -Algebraic对应物最近在[BCKW22]中获得。使用Ozawa的想法，我们表明，这种非同态结果也存在于von Neumann代数的水平上。
Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \not \simeq M_0(H_{\mathbb{R}})$ for $-1 < q \not = 0 < 1$. The C$^\ast$-algebraic counterpart of this result was obtained recently in [BCKW22]. Using ideas of Ozawa we show that this non-isomorphism result also holds on the level of von Neumann algebras.
