| 投影算子组的联合谱 |
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| 引用本文： | 吴文明,蒋叶聪,阮颖彬,钱文华. 投影算子组的联合谱[J]. 中国科学:数学, 2021, 0(5): 711-722 |
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| 作者姓名： | 吴文明 蒋叶聪 阮颖彬 钱文华 |
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| 作者单位： | 重庆师范大学数学科学学院;福建师范大学数信学院 |
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| 基金项目： | 国家自然科学基金(批准号:11871127,11801050,11671133和11971463);重庆市科委项目(批准号:cstc2019jcyj-msxmX0256);重庆市教委科学技术研究(批准号:KJQN2018000538)资助项目。 |
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| 摘 要： | 本文研究Hilbert空间H上投影算子组的联合谱.首先通过计算给出正则投影对的联合谱,进而给出一般的投影算子对的联合谱.本文还对两个投影算子的和与差的可逆性给出一些等价刻画.特别地,当P和Q为正则投影对时,本文通过计算算子组[I,P,Q]的联合谱来给出σ(P+Q)和σ(P-Q)的具体刻画.反过来,本文证明两类具有特定形...
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| 关 键 词： | 投影算子组 联合谱 正则投影对 |
The joint spectrum of a tuple of projections |
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| Wenming Wu,Yecong Jiang,Yingbin Ruan,Wenhua Qian. The joint spectrum of a tuple of projections[J]. Scientia Sinica Mathemation, 2021, 0(5): 711-722 |
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| Authors: | Wenming Wu Yecong Jiang Yingbin Ruan Wenhua Qian |
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| Abstract: | We study the joint spectrum of projections in a Hilbert space, and calculate the joint spectrum of a pair of projections. In particular, by calculating the joint spectrum for a tuple [I, P, Q] in which I is the identity and P, Q is a regular pair of projections, we get specific characterizations of the spectrums of P + Q and P-Q,respectively. Conversely, we prove that two closed subsets of C in particular forms are respectively the spectrums of the sum and the difference of a regular pair of projections. We also calculate the joint spectrum of a 3-tuple of projections [P, Q, R] for P, Q and R satisfying some specific conditions. |
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| Keywords: | tuple of projections joint spectrum regular pair of projections |
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