Abstract
We prove thet a Banach space X has the \(\lambda \)-bounded compact approximation property (respectively, weak \(\lambda \)-bounded approximation property) if and only if X has the \(\lambda \)-Lipschitz bounded compact approximation property (respectively, weak \(\lambda \)-Lipschitz bounded approximation property). Also, it is shown that the dual space of X has the approximation property if and only if for every separable reflexive Banach space Y, the space of finite rank Lipschitz maps from X to Y is dense in the Lipschitz norm in the space of compact operators from X to Y.
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J. M. Kim was supported by National Research Foundation of Korea (NRF-2021R1F1A1047322).
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Kim, J.M. Some Results on Approximation Properties of Lipschitz Maps. Results Math 79, 125 (2024). https://doi.org/10.1007/s00025-024-02155-x
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DOI: https://doi.org/10.1007/s00025-024-02155-x