All Questions
4 questions
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Bound on covering number of Lipschitz functions – missing part in proofs of Kolmogorov et al
Given a metric space $(\mathcal{X},\rho)$ and $\mathcal{A}\subset\mathcal{X}$ totally bounded, i.e. $\mathcal{A}$ has a finite $\varepsilon$-covering for any $\varepsilon>0$. Consider $\...
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Existence of a Gelfand triple involving the Arens–Eells space (aka Lipschitz free space)
$\DeclareMathOperator\Lip{Lip}\DeclareMathOperator\AE{AE}$Background
Gelfand triples. Let $\mathcal B$ be a Banach space, $\mathcal B^*$ its dual space, and $\mathcal H$ a Hilbert space. The triple $(\...
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Perturbing the approximation property from the Lipschitz-free space to stay in the Wasserstein space
Let $(X,d,x)$ be a separable pointed metric space and let $\mathcal{F}(X)$ be its Arens-Eells (also called its Lipschitz-Free space; in the case where $X$ is Banach) space. We view the $1$-...
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Dual Banach space $X^*$ complemented in $\mathrm{Lip}_0(X)$?
$\DeclareMathOperator\Lip{Lip}$Let $X$ be a real Banach space. The dual $X^*$ is a closed subspace of $\Lip_0(X)$. ($\Lip_0(X)$ denotes the space of real-valued Lipschitz functions $f:X\to\mathbb{R}$ ...
