论文标题
操作员代数原则
Principles of operator algebras
论文作者
论文摘要
这是对线性运算符$ t：h \ to H $可以形成的代数$ a \ subset b（h）$的介绍，一旦给出了复杂的希尔伯特空间$ h $。由量子力学的激励，我们主要对von Neumann代数感兴趣，von Neumann代数稳定，在伴随下，$ t \ to t^*$，并且较弱地关闭。当代数具有跟踪$ tr：a \ to \ mathbb c $时，我们可以将其视为$ a = l^\ infty（x）$的形式，而$ x $是量子测量的空间。特别值得关注的是免费案例，代数的中心减少到标量为$ z（a）= \ mathbb c $。在Von Neumann，Connes，Jones，Voiculescu等之后，我们讨论了此类代数$ a $的基本属性，以及如何在基础量子空间$ x $上进行代数，几何，分析和概率。
This is an introduction to the algebras $A\subset B(H)$ that the linear operators $T:H\to H$ can form, once a complex Hilbert space $H$ is given. Motivated by quantum mechanics, we are mainly interested in the von Neumann algebras, which are stable under taking adjoints, $T\to T^*$, and are weakly closed. When the algebra has a trace $tr:A\to\mathbb C$, we can think of it as being of the form $A=L^\infty(X)$, with $X$ being a quantum measured space. Of particular interest is the free case, where the center of the algebra reduces to the scalars, $Z(A)=\mathbb C$. Following von Neumann, Connes, Jones, Voiculescu and others, we discuss the basic properties of such algebras $A$, and how to do algebra, geometry, analysis and probability on the underlying quantum spaces $X$.
