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Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang

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Abstract

Motivated by a paper of Fang (2009), we study the Samuel multiplicity and the structure of essentially semi-regular operators on an infinite-dimensional complex Banach space. First, we generalize Fang’s results concerning Samuel multiplicity from semi-Fredholm operators to essentially semi-regular operators by elementary methods in operator theory. Second, we study the structure of essentially semi-regular operators. More precisely, we present a revised version of Fang’s 4 × 4 upper triangular model with a little modification, and prove it in detail after providing numerous preliminary results, some of which are inspired by Fang’s paper. At last, as some applications, we get the structure of semi-Fredholm operators which revised Fang’s 4 × 4 upper triangular model, from a different viewpoint, and characterize a semi-regular point λ ∈ ℂ in an essentially semi-regular domain.

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Authors and Affiliations

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

    QingPing Zeng & HuaiJie Zhong

  2. Fuzhou Strait Vocation Technological College, Fuzhou, 350014, China

    ZhenYing Wu

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  1. QingPing Zeng
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  2. HuaiJie Zhong
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  3. ZhenYing Wu
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Correspondence to QingPing Zeng.

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Zeng, Q., Zhong, H. & Wu, Z. Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang. Sci. China Math. 56, 1213–1231 (2013). https://doi.org/10.1007/s11425-012-4508-6

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  • DOI: https://doi.org/10.1007/s11425-012-4508-6

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