Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang
Samuel multiplicity and the structure of essentially semi-regular operators: A note on a paper of Fang
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DOI：
10.1007/s11425-012-4508-6
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
Qingping Zeng;H. Zhong;Zhenying Wu
中科院分区：
文献类型：
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作者：
Qingping Zeng;H. Zhong;Zhenying Wu
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 pointλ∈ ℂ in an essentially semi-regular domain.
