Related papers: Some comments on Laakso graphs and sets of differe…

The existence of a counterexample to the infinite-dimensional Carleson embedding theorem has been established by Nazarov, Pisier, Treil, and Volberg. We provide an explicit construction of such an example. We also obtain a non-constructive…

We prove that $L(X,Y)$ is complemented in $Lip_0(X, Y)$ (via a norm-one projection) provided that $Y$ is a dual space. Next, we introduce a vector-valued Lipschitz-free space $F_Y(X)$, a linear contraction $\beta_X^Y: F_Y(X) \to Y$ and…

In this article we start a systematic study of the bi-Lipschitz geometry of lamplighter graphs. We prove that lamplighter graphs over trees bi-Lipschitzly embed into Hamming cubes with distortion at most~$6$. It follows that lamplighter…

Blair, Campisi, Taylor, and Tomova defined the L-invariant L(F) of a knotted surface F, using pants complexes of trisection surfaces of bridge trisections of F. After that, Aranda, Pongtanapaisan, and Zhang introduced the L*-invariant L*(F)…

We show that a locally finite, connected graph has a coarse embedding into a Hilbert space if and only if there exist bond percolations with arbitrarily large marginals and two-point function vanishing at infinity. We further show that the…

One can define Fourier multipliers on a Banach function space by using the direct and inverse Fourier transforms on $L^2(\mathbb{R}^n)$ or by using the direct Fourier transform on $S(\mathbb{R}^n)$ and the inverse one on $S'(\mathbb{R}^n)$.…

The purpose of this note is to scrutinize the proof of Burago and Zalgaller regarding the existence of $PL$ isometric embeddings of $PL$ compact surfaces into $\mathbb{R}^3$. We conclude that their proof does not admit a direct extension to…

Given a metric space $(X,d)$, a set of terminals $K\subseteq X$, and a parameter $t\ge 1$, we consider metric structures (e.g., spanners, distance oracles, embedding into normed spaces) that preserve distances for all pairs in $K\times X$…

We continue the study dilation of linear maps on vector spaces introduced by Bhat, De, and Rakshit. This notion is a variant of vector space dilation introduced by Han, Larson, Liu, and Liu. We derive vector space versions of Wold…

In constructive mathematics the metric complement of a subset S of a metric space X is the set -S of points in X that are bounded away from S. In this note we discuss, within Bishop's constructive mathematics, the connection between the…

We introduce and study $\alpha$-embedded sets and apply them to generalize the Kuratowski Extension Theorem.

We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also…

We show that the Hilbert transform does not map $L^1(M_{\Phi}w)$ to $L^{1,\infty}(w)$ for every Young function $\Phi$ growing more slowly than $t\log\log ({\rm e}^{\rm e}+t)$. Our proof is based on a construction of M.C. Reguera and C.…

We study the nonlinear embeddability of Banach spaces and the equi-embeddability of the family of Kalton's interlaced graphs $([\mathbb N]^k,d_{\mathbb K})_k$ into dual spaces. Notably, we define and study a modification of Kalton's…

Let $X$ be a given Banach space and let $M$, $N$ be two orthogonal $X$-valued local martingales such that $N$ is weakly differentially subordinate to $M$. The paper contains the proof of the estimate $$ \mathbb E \Psi(N_t) \leq…

Let f(t,X) be an irreducible polynomial over the field of rational functions k(t), where k is a number field. Let O be the ring of integers of k. Hilbert's irreducibility theorem gives infinitely many integral specializations of t to values…

Bruns and Roddy constructed a $3$-generated modular ortholattice $L$ which cannot be embedded into any complete modular ortholattice. Motivated by their approach, we use shift operators to construct a $*$-regular $*$-ring $R$ of…

We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special…

We show that if a countably generated Lie algebra $H$ does not contain isomorphic copies of certain finite-dimensional nilpotent Lie algebras $A$ and $B$ (satisfying some mild conditions), then $H$ embeds into a quotient of $A \ast B$ that…

See title. (A Banach space is said to be L-embedded if it is complemented in its bidual such that the norm between the two complementary subspaces is additive.)