Related papers: Connes' Embedding Problem and Lance's WEP

Using free random varaibles we find an embedding of the operator space $OH$ in the predual of a von Neumann algebra. The properties of this embedding allow us to determined the projection constant of $OH_n$, i.e. there exists a projection…

Using the natural action of $S_\infty$ we show that a countable hereditary class $\mathcal C$ of finitely generated structures has the joint embedding property (JEP) and the weak amalgamation property (WAP) if and only if there is a…

In many applications, particularly in the natural sciences, the available high-dimensional set of features may contain variables that are not correlated with the response under consideration. Such irrelevant features can, in certain cases,…

This paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other…

The purpose of this note is to extend the extrapolation result by by Cruz-Uribe Martell and P\'erez as follows. Given a family $\mathcal{F}$ of pairs of functions suppose that for some $0<p<\infty$ and for every $w\in A_{\infty}$…

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

A necessary and sufficient condition for an inner function F in the upper half-plane (UHP) to satisfy F = E*/E where E is a de Branges function is presented. Since F_E =E^*/E is an inner function for any de Branges function E, and the map…

The second part of the paper mainly deals with convergence of infinite determinantal measures, understood as the convergence of the approximating finite determinantal measures. In addition to the usual weak topology on the space of…

Given $1< p < q < \infty$ it is well know that the natural embedding of Lebesgue sequence spaces $\ell_p \hookrightarrow \ell_q$ is strictly singular. In this paper we extend this classical results and show that even the natural non-compact…

Based on the fact that, for a subfactor $N$ of a II$_1$ factor $M,$ the first non-trivial Jones index is 2 and then $M$ is decomposed as the crossed product of $N$ by an outer action of ${\mathbb{Z}}_2,$ we study pairs $ \{N, uNu^* \}$ from…

We show that the $\ell_2$ norm of a static sense embedding encodes information related to the frequency of that sense in the training corpus used to learn the sense embeddings. This finding can be seen as an extension of a previously known…

Using various finite dimensional approximation properties, four convex subsets of the tracial space of a unital C*-algebra are defined. Applications of these tracial invariants include: (1) An analogue of Szego's limit theorem for arbitrary…

We present a new proof of Zippin's Embedding Theorem, that every separable reflexive Banach space embeds into one with shrinking and boundedly complete basis, and every Banach space with a separable dual embeds into one with a shrinking…

We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally…

We undertake a systematic study of W*-rigidity paradigms for the embeddability relation $\hookrightarrow$ between separable II$_1$ factors and its stable version $\hookrightarrow_s$, obtaining large families of non stably isomorphic II$_1$…

My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to…

In this paper we study conditions under which, for an inclusion of finite von Neumann algebras $N \subseteq M$, we have the reduced amalgamated free product $\ast_N M$ is embeddable into $(R \bar{\otimes} N_1)^\omega$ for some other finite…

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…

We consider the group $\mathfrak{X}(G)$ obtained from $G\ast G$ by forcing each element $g$ in the first free factor to commute with the copy of $g$ in the second free factor. Deceptively complicated finitely presented groups arise from…

In this note we show that for analytic semigroups the so-called Weiss condition of uniform boundedness of the operators $Re(\lambda)^\einhalb C(\lambda+A)^{-1}, \qquad Re(\lambda)>0$ on the complex right half plane and weak Lebesgue…