ADDITIVE MAPPINGS PRESERVING FREDHOLM OPERATORS WITH FIXED NULLITY OR DEFECT

doi:10.1007/s10473-021-0516-3

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (5): 1670-1678.doi: 10.1007/s10473-021-0516-3

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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).

Abstract

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

CLC Number:

15A86

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

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