ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

doi:10.1007/s10473-021-0516-3

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (5): 1670-1678.doi: 10.1007/s10473-021-0516-3

ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

张芮涵, 史维娟, 吉国兴

School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China

收稿日期:2019-09-30 修回日期:2021-04-14 出版日期:2021-10-25 发布日期:2021-10-21
通讯作者: Weijuan SHI E-mail:shiweijuan1016@163.com
作者简介:Ruihan ZHANG,E-mail:ruihan@snnu.edu.cn;Guoxing JI,E-mail:gxji@snnu.edu.cn
基金资助:
This research was supported by National Natural Science Foundation of China (11771261, 11701351), Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1082) and the Fundamental Research Funds for the Central Universities (GK202103007, GK202107014).

ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

Ruihan ZHANG, Weijuan SHI, Guoxing JI

School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China

Received:2019-09-30 Revised:2021-04-14 Online:2021-10-25 Published:2021-10-21
Contact: Weijuan SHI E-mail:shiweijuan1016@163.com
Supported by:
This research was supported by National Natural Science Foundation of China (11771261, 11701351), Natural Science Basic Research Plan in Shaanxi Province of China (2018JQ1082) and the Fundamental Research Funds for the Central Universities (GK202103007, GK202107014).

摘要/Abstract

摘要： Let $\mathcal{X}$ be an infinite-dimensional real or complex Banach space, and $\mathcal{B}(\mathcal{X})$ the Banach algebra of all bounded linear operators on $\mathcal{X}$. In this paper, given any non-negative integer $n$, we characterize the surjective additive maps on $\mathcal{B}(\mathcal{X})$ preserving Fredholm operators with fixed nullity or defect equal to $n$ in both directions, and describe completely the structure of these maps.

关键词: Fredholm operator, additive preserver, nullity, defect

Abstract: Let $\mathcal{X}$ be an infinite-dimensional real or complex Banach space, and $\mathcal{B}(\mathcal{X})$ the Banach algebra of all bounded linear operators on $\mathcal{X}$. In this paper, given any non-negative integer $n$, we characterize the surjective additive maps on $\mathcal{B}(\mathcal{X})$ preserving Fredholm operators with fixed nullity or defect equal to $n$ in both directions, and describe completely the structure of these maps.

Key words: Fredholm operator, additive preserver, nullity, defect

中图分类号:

15A86

张芮涵, 史维娟, 吉国兴. ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT[J]. 数学物理学报(英文版), 2021, 41(5): 1670-1678.

Ruihan ZHANG, Weijuan SHI, Guoxing JI. ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT[J]. Acta mathematica scientia,Series B, 2021, 41(5): 1670-1678.

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ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

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