Banach spaces of Lipschitz functions - AOUFI, khayra (Faculty of Mathematics and Computer Sciences Department of Mathematics - Option : Functional Analysis, 2020)
In this work, we tackle Lipschitz space Lip0 (X), that X is a pointed metric space, and it is dual. We study the preduals Æ(X) and F (X), that are isometrics in addition to its properties. Then we study the space lip0 (X), which is under certain conditions of X is a predual of Æ(X). We end this work, by introducing B-Lipschitz summing operators.
Keywords: Metric space, Lipschitz space, Arens-Eells space, Free Banach space, The little Lipschitz space, B-Lipschitz summing operators.