论文标题
在$ q $ -Gaussian c $^\ ast $ -Algebras的同构级上无限变量
On the isomorphism class of $q$-Gaussian C$^\ast$-algebras for infinite variables
论文作者
论文摘要
对于真正的希尔伯特太空$ h _ {\ mathbb {r}} $和$ -1 <q <1 $ bozejko和speicher介绍了c $^\ ast $ -algebra $ a_q（ $ m_q（h _ {\ mathbb {r}}）$ $ q $ -gaussian变量。我们证明，如果$ \ dim（H _ {\ Mathbb {r}}）= \ infty $和$ -1 <q <q <1，q \ not = 0 $，则$ m_q（h _ {\ Mathbb {r}} $因此，$ a_q（h _ {\ mathbb {r}}）$不是$ a_0（h _ {\ mathbb {r}}}）$的异态。这给出了问题1.1的C $^\ AST $ -Algebraic部分，并在[Neze18]中的问题1.2。
For a real Hilbert space $H_{\mathbb{R}}$ and $-1 < q < 1$ Bozejko and Speicher introduced the C$^\ast$-algebra $A_q(H_{\mathbb{R}})$ and von Neumann algebra $M_q(H_{\mathbb{R}})$ of $q$-Gaussian variables. We prove that if $\dim(H_{\mathbb{R}}) = \infty$ and $-1 < q < 1, q \not = 0$ then $M_q(H_{\mathbb{R}})$ does not have the Akemann-Ostrand property with respect to $A_q(H_{\mathbb{R}})$. It follows that $A_q(H_{\mathbb{R}})$ is not isomorphic to $A_0(H_{\mathbb{R}})$. This gives an answer to the C$^\ast$-algebraic part of Question 1.1 and Question 1.2 in [NeZe18].
