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The approximate Jordan forms of operators on Σ 1 e type Banach spaces

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Abstract

This paper studies the structure of operators on Σ 1 e type Banach spaces. It solves the problem of the small compact perturbations of operators with connected spectra. Namely, it shows that every operator with a connected spectrum on separable Σ 1 e type Banach spaces is a small compact perturbation of a strongly irreducible operator. Based on this result, this paper establishes the approximate Jordan forms of operators on Σ 1 e type Banach spaces with Schauder bases.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    YunNan Zhang, LiQiong Lin & HuaiJie Zhong

  2. Mathematics and Information Science College, Hebei Normal University, Shijiazhuang, 050016, China

    YunNan Zhang

  3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350002, China

    LiQiong Lin

Authors
  1. YunNan Zhang
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  2. LiQiong Lin
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  3. HuaiJie Zhong
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Correspondence to LiQiong Lin.

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Zhang, Y., Lin, L. & Zhong, H. The approximate Jordan forms of operators on Σ 1 e type Banach spaces. Sci. China Math. 54, 723–740 (2011). https://doi.org/10.1007/s11425-010-4149-6

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  • DOI: https://doi.org/10.1007/s11425-010-4149-6

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