Related papers: A Radon-Nikodym theorem for von Neumann algebras

In this work, we systematically derive the Einstein field equations in general relativity and $f(\mathcal{R})$ gravity, the Tolman-Oppenheimer-Volkoff (TOV) equation, and the expressions for axial and polar Tidal Love Numbers (TLNs) for…

For $n\geq 3,$ let $\Gamma=SL_n(\mathbb Z).$ We prove the following superridigity result for $\Gamma$ in the context of operator algebras. Let $L(\Gamma)$ be the von Neumann algebra generated by the left regular representation of $\Gamma.$…

We investigate Cartan subalgebras in nontracial amalgamated free product von Neumann algebras $M_1 \ast_B M_2$ over an amenable von Neumann subalgebra $B$. First, we settle the problem of the absence of Cartan subalgebra in arbitrary free…

We present a natural and simple proof of the Radon - Nikodym theorem for measures with values in the space of bounded linear operators on a separable Hilbert space. This space is not separable, that is why it is essential to assume in the…

In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…

Given a von Neumann algebra $M$ with a faithful normal semi-finite trace $\tau,$ let $L(M, \tau)$ be the algebra of all $\tau$-measurable operators affiliated with $M.$ We prove that if $A$ is a locally convex reflexive complete metrizable…

We investigate the topological nilpotence degree, in the sense of Henn-Lannes-Schwartz, of a connected Noetherian unstable algebra $R$. When $R$ is the mod $p$ cohomology ring of a compact Lie group, Kuhn showed how this invariant is…

There is undetermined potential function $V(\phi)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a…

Growing out of the initial connections between subfactors and knot theory that gave rise to the Jones polynomial, Jones' axiomatization of the standard invariant of an extremal finite index $II_1$ subfactor as a spherical $C^*$-planar…

The notions of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and with odd formal variables and of N=1 Neveu-Schwarz vertex operator superalgebra over a Grassmann algebra and without odd formal variables are…

Let $(M, \varphi) = (M_1, \varphi_1) \ast (M_2, \varphi_2)$ be a free product of arbitrary von Neumann algebras endowed with faithful normal states. Assume that the centralizer $M_1^{\varphi_1}$ is diffuse. We first show that any…

The aim of this paper is to explore the complexity factor (CF) for those self-gravitating relativistic spheres whose evolution proceeds non-dynamically. We are adopting the definition of CF mentioned in \cite{PhysRevD.97.044010}, modifying…

Suppose $\mathscr M$ and $\mathscr N$ are von Neumann algebras. Two operators $A$ and $B$ in $\mathscr M$ are said to be orthogonal if $A^*B=0$, meaning their ranges are orthogonal. Let $\varphi\colon\mathscr M\to\mathscr N$ be a map. We…

In this work, we show that a class of metric-affine gravities can be reduced to a Riemann-Cartan one. The reduction is based on the cancelation of the nonmetricity against the symmetric components of the spin connection. A heuristic proof,…

We consider the class non-surjective irreducible endomorphisms of the free group $F_n$. We show that such an endomorphism $\phi$ is topologically represented by a simplicial immersion $f:G \rightarrow G$ of a marked graph $G$; along the way…

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible…

We use ergodic theoretic tools to solve a classical problem in geometric Ramsey theory. Let E be a measurable subset of R^m, with positive upper density. Let V={0,v_1,...,v_k} be a subset of R^m. We show that for r large enough, we can find…

We show that the algebraic K-theory of semi-valuation rings with stably coherent regular semi-fraction ring satisfies homotopy invariance. Moreover, we show that these rings are regular if their valuation is non-trivial. Thus they yield…

In this article, we aim to provide a satisfactory algebraic description of the set of affiliated operators for von Neumann algebras. Let $\mathscr{M}$ be a von Neumann algebra acting on a Hilbert space $\mathcal{H}$, and let…

We let U=SU(2) and K=SO(2) and denote N_{U}(K) the normalizer of K in U. For a an element of U\ N_{U} (K), we let \mu_{a} be the normalized singular measure supported in KaK. For p a positive integer, it was proved that \mu_{a}^{( p)}, the…