Abstract
In this paper, we provide an infinite metric space M such that the set SNA(M) of strongly norm-attaining Lipschitz functions on M does not contain a subspace which is linearly isometric to c0. This answers a question posed by Antonio Avilés, Gonzalo Martínez-Cervantes, Abraham Rueda Zoca, and Pedro Tradacete. On the other hand, we prove that SNA(M) contains an isometric copy of c0 whenever M is an infinite metric space which is not uniformly discrete. In particular, the latter holds true for all infinite compact metric spaces while it does not hold true for all proper metric spaces. We also provide some positive results in the non-separable setting.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
