两个酉算子的线性组合与框架分解

• 作 者: 李祚 朱红鲜 张慧 杜鸿科
• 机 构: College of Science, Xi’an University of Architecture and Technology, Xi’an, 710055
• 出 处: 东北数学（英文版）
• 发表日期: 2005年2期
• 关键词: polar decomposition semi-Fredholm spectral decomposition frame representation

In this paper, we prove that the norm closure of all linear combinations oftwo unitary operators is equal to the norm closure of all invertible operators inB(H).We apply the results to frame representations and give some simple and alternativeproofs of the propositions in “P. G. Casazza, Every frame is a sum of three (but nottwo) orthonormal bases-and other frame representations, J. Fourier Anal. Appl.,4(6)(1998), 727-732.”