Characterizations of bounded compact approximation property by Calkin representations
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- by Dongyang Chen
- Proc. Amer. Math. Soc. 150 (2022), 5397-5402
- DOI: https://doi.org/10.1090/proc/16056
- Published electronically: July 15, 2022
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Uncorrected version: Original version posted July 15, 2022
Corrected version: This version replaces the original article due to author error.
Abstract:
In this note we characterize the bounded compact approximation property via Calkin representations for Banach spaces.References
- Kari Astala and Hans-Olav Tylli, On the bounded compact approximation property and measures of noncompactness, J. Funct. Anal. 70 (1987), no. 2, 388–401. MR 874062, DOI 10.1016/0022-1236(87)90118-2
- H. Behncke, On the Calkin representations of $B({\scr H})$, Proc. Amer. Math. Soc. 101 (1987), no. 1, 101–107. MR 897078, DOI 10.1090/S0002-9939-1987-0897078-1
- March T. Boedihardjo and William B. Johnson, On mean ergodic convergence in the Calkin algebras, Proc. Amer. Math. Soc. 143 (2015), no. 6, 2451–2457. MR 3326027, DOI 10.1090/S0002-9939-2015-12432-X
- J. W. Calkin, Two-sided ideals and congruences in the ring of bounded operators in Hilbert space, Ann. of Math. (2) 42 (1941), 839–873. MR 5790, DOI 10.2307/1968771
- Arnold Lebow and Martin Schechter, Semigroups of operators and measures of noncompactness, J. Functional Analysis 7 (1971), 1–26. MR 0273422, DOI 10.1016/0022-1236(71)90041-3
- G. A. Reid, On the Calkin representations, Proc. London Math. Soc. (3) 23 (1971), 547–564. MR 293413, DOI 10.1112/plms/s3-23.3.547
Bibliographic Information
- Dongyang Chen
- Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
- Email: cdy@xmu.edu.cn
- Received by editor(s): November 10, 2021
- Received by editor(s) in revised form: February 22, 2022
- Published electronically: July 15, 2022
- Additional Notes: This work was supported by the National Natural Science Foundation of China (Grant No. 11971403) and the Natural Science Foundation of Fujian Province of China (Grant No. 2019J01024)
- Communicated by: Stephen Dilworth
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 5397-5402
- MSC (2020): Primary 46B08, 47A35, 47B07
- DOI: https://doi.org/10.1090/proc/16056
- MathSciNet review: 4494612