Abstract:In this paper, we provide an infinite metric space M such that the set SNA(M ) of strongly norm-attaining Lipschitz functions does not contain a subspace which is isometric to c 0 . 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 c 0 whenever M is a metric space which is not uniformly discrete. In particular, the latter holds true for infinite compact metric spaces while … Show more
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