Quasi-diagonality and approximate innerness of flows on C*-algebras

冯·诺伊曼在量子力学的基础上成功地提出了希尔伯特空间的算符理论。他后来发展了算子环（或代数）理论，可能被认为是无限自由度量子力学的基础，如量子场论，但他没有完成这个项目，因为他被其他职业分散了注意力。在第二次世界大战结束前后，Gel’fand， Naimark和Segal提出了C*代数理论，并断言这是我们所追求的方案，作为无限自由度量子物理的框架。这个项目就是建立在这个基础上的，目的是研究C*-代数上随着时间的发展而出现的流动。我们建立了许多应该在物理模型中出现的近似内流和准对角流的性质，其中包括前者，看起来更容易接受。

von Neumann successfully placed the theory of operators on Hilbert space in the foundation of quantum mechanics. He later developed the theory of operator rings (or algebras), probably thought of as a foundation of quantum mechanics of infinite degree of freedom such as quantum field theory, but he never completed that project by being distracted by other callings. Around the ending of WWII Gel'fand, Naimark and Segal initiated the theory of C*-algebras and asserted it was the scheme we were after as a framework of quantum physics of infinite degrees of freedom. This project was built up on this claim and was to investigate flows on C*-algebras as appearing as time-developments. We established many properties of approximately inner flows which were supposed to appear in physical models, and quas-diagonal flows, which include the formers and look more amenable.