Related papers: Low distortion embeddings between $C(K)$ spaces

We prove the sharp embedding between the spectral Barron space and the Besov space with embedding constants independent of the input dimension. Given the spectral Barron space as the target function space, we prove a dimension-free…

We prove that for every $\epsilon\in (0,1)$ there exists $C_\epsilon\in (0,\infty)$ with the following property. If $(X,d)$ is a compact metric space and $\mu$ is a Borel probability measure on $X$ then there exists a compact subset…

We show that for every large enough integer $N$, there exists an $N$-point subset of $L_1$ such that for every $D>1$, embedding it into $\ell_1^d$ with distortion $D$ requires dimension $d$ at least $N^{\Omega(1/D^2)}$, and that for every…

We find all values of $k\in \mathbb C$, for which the embedding of the maximal affine vertex algebra in a simple minimal W-algebra $W_k(\mathfrak g,\theta)$ is conformal, where $\mathfrak g$ is a basic simple Lie superalgebra and $-\theta$…

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.

In this paper, we describe a family of embedded hypersurfaces with constant mean curvature (CMC) in the $(n+1)$-dimensional unit sphere. In the process, we provide evidence for new CMC embedded examples. In particular, for some examples…

Given metric spaces $(X,d)$ and $(Y,\rho)$ and an ordering $x_1,x_2,\ldots,x_n$ of $(X,d)$, an embedding $f: X \rightarrow Y$ is said to have a prioritized distortion $\alpha(\cdot)$, if for any pair $x_j,x'$ of distinct points in $X$, the…

Let $d \ge 2$, and let $K \subset {\Bbb{R}}^d$ be a convex body containing the origin $0$ in its interior. In a previous paper we have proved the following. The body $K$ is $0$-symmetric if and only if the following holds. For each $\omega…

The Kirchberg Embedding Problem (KEP) asks if every C*-algebra embeds into an ultrapower of the Cuntz algebra $\mathcal{O}_2$. In an effort to provide a negative solution to the KEP and motivated by the recent refutation of the Connes…

In this paper, the concepts of $K$-subset systems and $k$-well-filtered spaces are introduced, which provide another uniform approach to $d$-spaces, $s$-well-filtered spaces (i.e., $\mathcal{U}_{S}$-admissibility) and well-filtered spaces.…

We study non-trivial deformations of the natural imbedding of the Lie algebra $\fh_1$ of lower triangular matrices (the Heisenberg Lie algebra) into $gl(3,\mathbb{K})$, where $\mathbb{K}=\mathbb{R}$ or $|mathbb{C}$. Our first result is the…

The aim of this paper is to prove that if a planar set $A$ has a difference set $\Delta(A)$ satisfying $\Delta(A)\subset \Z^++s$ for suitable $s$ than $A$ has at most 3 elements. This result is motivated by the conjecture that the disk has…

For ell a generic n-tuple of positive numbers, N(ell) denotes the space of isometry classes of oriented n-gons in R^3 with side lengths specified by ell. We determine the algebra K(N(ell)) and use this to obtain nonimmersions of the…

This paper deals with the fractional Sobolev spaces $W^{s, p}(\Omega)$, with $s\in (0, 1]$ and $p\in[1,+\infty]$. Here, we use the interpolation results in [4] to provide suitable conditions on the exponents $s$ and $p$ so that the spaces…

Fix $k \in \mathbb{N}$ and $0 < \delta < 1$. We study how large $N$ must be so that every $\delta$-dense subset $\mathcal{D} \subset \{0,1\}^N$ (meaning $|\mathcal{D}| \geq \delta 2^N$) contains the image of a metric embedding $f: \{0,1\}^k…

We prove that for any given integer $c>0$ any metric space on $n$ points may be isometrically embedded into $l_{\infty}^{n-c}$ provided $n$ is large enough.

We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper…

We show that, given a compact Hausdorff space $\Omega$, there is a compact group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a complete…

In this note we show through infinitary derivations that each provably well-founded strict partial order in ${\rm ACA}_{0}$ admits an embedding to an ordinal$<\varepsilon_{0}$.

Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…