$K(\ell _p,\ell _q)$ is a Lipschitz retract of $B(\ell _p,\ell _q)$
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- by Lixin Cheng, Wuyi He and Sijie Luo PDF
- Proc. Amer. Math. Soc. 150 (2022), 3915-3925 Request permission
Abstract:
For two Banach spaces $X$ and $Y$, we denote by $K(X,Y)$ (resp. $B(X,Y)$) the space of all compact (resp. bounded) linear operators from $X$ to $Y$. In this paper, we show that for $1\leq p,q<\infty$, $K(\ell _{p},\ell _{q})$ is an 8-Lipschitz retract of $B(\ell _{p},\ell _{q})$.References
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Additional Information
- Lixin Cheng
- Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
- Email: lxcheng@xmu.edu.cn
- Wuyi He
- Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
- Email: wuyihe@stu.xmu.edu.cn
- Sijie Luo
- Affiliation: School of Mathematics and Statistics, Central South University, Changsha 410000, People’s Republic of China
- MR Author ID: 1244435
- ORCID: 0000-0001-9587-4402
- Email: sijieluo@csu.edu.cn
- Received by editor(s): August 10, 2021
- Received by editor(s) in revised form: September 4, 2021, November 5, 2021, and December 3, 2021
- Published electronically: April 14, 2022
- Additional Notes: The first author was partially supported by National Natural Science Foundation of China, grant no. 11731010.
The second author was partially supported by National Natural Science Foundation of China, grant no. 11731010.
The third author was partially supported by National Natural Science Foundation of China, grant no. 12071240. - Communicated by: Stephen Dilworth
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3915-3925
- MSC (2020): Primary 46B80; Secondary 46A32, 46B20, 46B28
- DOI: https://doi.org/10.1090/proc/15970
- MathSciNet review: 4446240