Kadison Richard V
Mathematics Department, University of Pennsylvania, Philadelphia, PA 19104-6395, USA.
Proc Natl Acad Sci U S A. 2002 Apr 2;99(7):4178-84. doi: 10.1073/pnas.032677199.
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both "discrete" and "continuous."
对毕达哥拉斯定理及其变体进行了研究。这些变体演变成一种基于冯·诺依曼代数上的非交换条件期望的表述形式，该表述将此定理展现为非交换度量欧几里得几何的基本结果。本文重点在于有限维性，包括“离散”和“连续”的有限维性。
