Operator Algebras, Interpolation and Frames

算子代数、插值和框架

• 批准号: 0300128
• 负责人: Vern Paulsen
• 金额: $ 11.5万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0300128&HistoricalAwards=false
• 关键词: Operator; Algebras; Interpolation; Frames

AbstractPaulsenMy research will focus in three directions. I will continue to study injective envelopes, seeking deeper results about their structure and further applications of these objects to the study of operator spaces and C*-algebras. I will especially focus on attempting to develop a deeper understanding of the connections between injective envelopes and the weak expectation property. I will also continue to study applications of operator algebra techniques to the study of Nevanlinna-Pick type interpolation, especially focusing on the use of the C*-envelope and Schur ideals. The third direction that I will focus is the study of finite dimensional frames from the viewpoint of coding theory, especially the problem of determining optimal frames for certain coding theory problems.-My research on frames could have the broadest impact. Frames are used as a way to ensure accurate communication of analogue information in the presence of uncertainty, usually coming from a noisy communication channel. My work on frames from a coding theory point of view intends to find the optimal frames to use for transmitting data, when it is anticipated that some of the data will be lost during the transmission. My work is especially relevant to the problem of "lost packages". Here one assumes that the data is packaged into discrete "bundles" that are then transmitted separately, perhaps even over different channels, and then reassembled later. The problem is what to do if only some of the bundles arrive? Clearly, one wants to build some redundancy into the transmitted data so that one can still reassemble a message, that if not exactly the original message, is close to the original message in some sense.

AbstractPaulsenmy研究将集中在三个方向上。我将继续研究注射式信封，为其结构以及这些对象的进一步应用而在操作员空间和c* - 代数研究中的进一步应用。我将特别专注于试图对注射信封与弱期望属性之间的联系有更深入的了解。我还将继续研究操作员代数技术的应用，以研究Nevanlinna-Pick型插值研究，尤其是专注于C*-Envelope和Schur理想的使用。我将重点关注的第三个方向是从编码理论的角度研究有限维帧的研究，尤其是确定某些编码理论问题的最佳框架的问题。我对框架的研究可能会产生最大的影响。框架被用作确保在不确定性存在下准确地进行模拟信息的一种方式，通常来自嘈杂的通信渠道。我从编码理论的角度的框架上进行的工作打算在传输过程中找到用于传输数据的最佳帧。我的工作与“丢失的包裹”问题特别相关。在这里，人们假设将数据打包到离散的“捆绑”中，然后分别传输，甚至通过不同的通道，然后重新组装。问题是只有一些捆绑包到来时该怎么办？显然，一个人希望在传输数据中构建一些冗余，以便仍然可以重新组装一条消息，即如果不是完全的原始消息，则在某种意义上与原始消息接近。