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The Lipschitz bounded approximation property for operator ideals

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Abstract

In this article, we introduce the Lipschitz bounded approximation property for operator ideals. With this notion, we extend the original work of Godefroy and Kalton and give some partial answers on equivalence between the bounded approximation property and the Lipschitz bounded approximation property based on an arbitrary operator ideal. Furthermore, we investigate the three space problem for the preceding bounded approximation properties.

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Acknowledgements

The authors would like to thank Yun Sung Choi, Ju Myung Kim and Abraham Rueda Zoca for fruitful conversations on the topic of the paper. The authors would also like to thank the anonymous referees for helpful comments and for pointing out a mistake in the previous version of this paper. G. Choi was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology [NRF-2020R1A2C1A01010377]. M. Jung was supported by NRF [NRF-2019R1A2C1003857] and by POSTECH Basic Science Research Institute Grant, whose NRF Grant number is 2021R1A6A1A10042944

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Authors and Affiliations

  1. Department of Mathematics Education, Dongguk University, Seoul, 04620, Republic of Korea

    Geunsu Choi

  2. Basic Science Research Institute and Department of Mathematics, POSTECH, Pohang, 790-784, Republic of Korea

    Mingu Jung

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  1. Geunsu Choi
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  2. Mingu Jung
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Correspondence to Mingu Jung.

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Communicated by Manuel Maestre.

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Choi, G., Jung, M. The Lipschitz bounded approximation property for operator ideals. Banach J. Math. Anal. 16, 10 (2022). https://doi.org/10.1007/s43037-021-00164-4

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  • DOI: https://doi.org/10.1007/s43037-021-00164-4

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