2024/06/22 by M. Raja, Raja, Matias
Mathematics · #advanced mathematical theories #Mathematical and Theoretical Analysis #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.2406.15779
The isometric universality of the spaces C(K) for K a non scattered Hausdorff compact does not take into account the ``quality'' of the representation. Indeed, the existence of an isometric copy of a separable Banach space X into C(K) made of regular enough functions, say Lipschitz with respect to a lower semicontinuous metric defined on K, imposes severe restrictions to both X and K. In this paper, we present a systematic treatment of the representation of Banach spaces into C(K) by Lipschitz functions improving previous results of the author.