Operators with the Lipschitz bounded approximation property
Abstract
We show that if a bounded linear operator can be approximated by a net (or sequence) of uniformly bounded finite rank Lipschitz mappings pointwisely, then it can be approximated by a net (or sequence) of uniformly bounded finite rank linear operators under the strong operator topology. As an application, we deduce that a Banach space has an (unconditional) Lipschitz frame if and only if it has an (unconditional) Schauder frame. Another immediate consequence of our result recovers the famous Godefroy-Kalton theorem (Godefroy and Kalton (2003)) which says that the Lipschitz bounded approximation property and the bounded approximation property are equivalent for every Banach space.
Publication Title
Science China Mathematics
Recommended Citation
Liu, R., Shen, J., & Zheng, B. (2023). Operators with the Lipschitz bounded approximation property. Science China Mathematics, 66 (7), 1545-1554. https://doi.org/10.1007/s11425-022-2000-y
