K-理论在一类算子逼近中的应用

文仕林, 何华

数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 717-730.

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数学学报 ›› 2015, Vol. 58 ›› Issue (5) : 717-730. DOI: 10.12386/A2015sxxb0073
论文

K-理论在一类算子逼近中的应用

    文仕林1, 何华2
作者信息 +

K-theory and Approximation of a Class of Operators

    Shi Lin WEN1, Hua HE2
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文章历史 +

摘要

构造了一类强不可约的Cowen-Douglas算子, 刻画了其换位代数的 K0-群. 我们证明了: 对于复可分的Hilbert 空间上的有界线性算子 T 及 ε>0, 总可以找到由有限多个强不可约的 Cowen-Douglas 算子构成的直和算子S, 使得‖T-S‖< ε.

Abstract

We construct a class of strongly irreducible Cowen-Douglas operators and characterize the K0-groups of their commutant algebras. Then we show that for each bounded linear operator T on a complex separable Hilbert space and ε > 0, there exists an operator S which can be written as a direct sum of finitely many strongly irreducible Cowen-Douglas operators with nice properties such that ‖T-S‖< ε.

关键词

Cowen-Douglas算子 / 换位代数 / K0-群 / 逼近

Key words

Cowen-Douglas operators / commutant algebra / K0-group / approximation

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文仕林, 何华. K-理论在一类算子逼近中的应用. 数学学报, 2015, 58(5): 717-730 https://doi.org/10.12386/A2015sxxb0073
Shi Lin WEN, Hua HE. K-theory and Approximation of a Class of Operators. Acta Mathematica Sinica, Chinese Series, 2015, 58(5): 717-730 https://doi.org/10.12386/A2015sxxb0073

参考文献

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[9] Jiang C. L., Wang Z. Y., Strongly Irreducible Operators on Hilbert Space, Research Notes in Math., 389 Pitman Books, 1998.

[10] Jiang C. L., Wang Z. Y., Structure of Hilbert Space Operators, World Scientific, Singapore, 2006.

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基金

国家自然科学基金资助项目(11171087)

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