Spaces of Lipschitz and H¨ older functions and their applications

By Nigel J. Kalton. 2004

68 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bac8c4cfd7c3dcb705087ffeaa33e8745630072d

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1. A. Dalet
2. Gilles Godefroy
3. G. Lancien
4. V. Kadets
5. Y. Ivakhno
6. V. Zizler
7. Alexandre Godard
8. Dirk Werner

Citations in the corpus

• Free Spaces Over Some Proper Metric Spaces (2014, background): “ it has the MAP. Thus it follows from Theorem 2.1 that it is enough to prove that for M a countable proper metric space, F(M) has the BAP. We need the following result we can deduce from Lemma 4.2 in [11]: For any pointed metric space M, define for N ∈ N, AN = B(0,2N+1)\B(0,2−N−1) ∪ {0}. Then there e”
• Tree metrics and their Lipschitz-free spaces (2009, background): “anonical examples of Lipschitz-free spaces isomorphic to a subspace of L1 (and therefore unique isometric predual by [6]). Examples of spaces F(M) which are unique isometric preduals are plentiful in [8]; N.J. Kalton shows the following result: if M is an arbitrary metric space and ε > 0, then th”
• The non-linear geometry of Banach spaces after Nigel Kalton (2012, background): “s. If f: Gk(N) → Xis bounded, define ∂f: Gk−1(N) → X∗∗ by ∀n∈ Gk−1(N) ∂f(n) = w∗ − lim nk∈U f(n1,..,nk−1,nk). We leave it to the reader to rewrite the argument. (3) On the other hand, Kalton proved in [52] that c0 embeds uniformly and coarsely in a Banach space X with the Schur property. Note that X ”
• THE DAUGAVET PROPERTY FOR SPACES OF LIPSCHITZ FUNCTIONS (2005, methodology): “entails a contradiction between (3.7) and properties (1) and (3) from the lemma. The space Lip(K) has a canonical predual, called the Arens-Eells space in [13] and the Lipschitz free space in [4] and [7]. Since we have used in (3.3), in the proof of Lemma 3.2, a functional from that predual, i.e., a”