来自数学物理的Kadison-Singer：简介
Kadison-Singer from mathematical physics: An introduction
摘要：
我们给出了一个非正式的概述的Kadison-Singer扩展问题，重点是它的初始连接到狄拉克的制定量子力学。设H是无限维可分希尔伯特空间，B（H）是H中所有有界算子的代数.在算子代数的语言中，Kadison-Singer问题询问对于B（H）中的给定MASA D，D上的每个纯态是否具有B（H）上的纯态的唯一扩展。换句话说，这些纯态扩展是唯一的吗？最近Pete Casazza和他的同事指出，这个问题与数学其他领域（调和分析、组合学（通过Anderson pavings）、巴拿赫空间理论、框架理论）和应用（信号处理、互联网编码、编码理论等）的中心开放问题密切相关。
英文摘要：
We give an informal overview of the Kadison-Singer extension problem with emphasis on its initial connections to Dirac's formulation of quantum mechanics. Let H be an infinite dimensional separable Hilbert space, and B(H) the algebra of all bounded operators in H. In the language of operator algebras, the Kadison-Singer problem asks whether or not for a given MASA D in B(H), every pure state on D has a unique extension to a pure state on B(H). In other words, are these pure-state extensions unique? It was shown recently by Pete Casazza and co-workers that this problem is closely connected to central open problems in other parts of mathematics (harmonic analysis, combinatorics (via Anderson pavings), Banach space theory, frame theory), and applications (signal processing, internet coding, coding theory, and more).
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