一类本性谱有界算子的刻画 |
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引用本文: | 吴校贵,张建华. 一类本性谱有界算子的刻画[J]. 数学学报, 2010, 53(4): 759-762 |
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作者姓名: | 吴校贵 张建华 |
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作者单位: | 陕西师范大学数学与信息科学学院 西安 710062 |
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基金项目: | 国家自然科学基金资助项目(10571114); 陕西省自然科学研究计划资助项目(2004A17) |
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摘 要: | 设H是一个无限维复Hilbert空间,B(H)表示H上的有界线性算子的全体,并且Φ是从B(H)到自身的线性满射.我们证明了映射Φ是本性谱有界且模紧算子的充分必要条件是Φ(K(H))■K(H)且诱导映射Φ是Calkin代数上的连续同态或连续反同态.
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关 键 词: | 谱有界 Calkin代数 Jordan同态 |
收稿时间: | 2009-06-26 |
修稿时间: | 2010-01-20 |
A Characterization of Certain Essentially Spectrally Bounded Operators |
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Affiliation: | College of Mathematics and Information Science, Shanxi Normal University, Xi'an 710062, P. R. China |
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Abstract: | Let H be an infinite-dimensional complex Hilbert space, B(H) be the algebra of all bounded linear operators on H, and Φ be a linear mapping from B(H) onto itself. We show that Φ is essentially spectrally bounded and surjective up to compact operators if and only if Φ(K(H))⊆K(H) and the induced mapping Ψ is a continuous homomorphism or continuous anti-homomorphism. |
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Keywords: | spectrally bounded Calkin algebra Jordan homomorphism |
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