单位紧框架的固定对角投影和幂等元及同伦问题
Projections and idempotents with fixed diagonal and the homotopy problem for unit tight frames
摘要：
本文研究了希尔伯特空间中关于固定规范正交基具有预定对角元的幂等算子和投影集合的拓扑和度量结构。作为应用，我们解决了Larson，Dykema和Strawn关于单位范数紧框架集合的连通性的一些情况。
英文摘要：
We investigate the topological and metric structure of the set of idempotent operators and projections which have prescribed diagonal entries with respect to a fixed orthonormal basis of a Hilbert space. As an application, we settle some cases of conjectures of Larson, Dykema, and Strawn on the connectedness of the set of unit-norm tight frames.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
