Artículos con la etiqueta ‘Operator Algebras (math.OA)’

Commuting and noncommuting infinitesimals

Por • 10 abr, 2013 • Category: Filosofía

Infinitesimals are natural products of the human imagination. Their history goes back to the Greek antiquity. Their role in the calculus and analysis has seen dramatic ups and downs. They have stimulated strong opinions and even vitriol. Edwin Hewitt developed hyperreal fields in the 1940s. Abraham Robinson’s infinitesimals date from the 1960s. A noncommutative version of infinitesimals, due to Alain Connes, has been in use since the 1990s. We review some of the hyperreal concepts, and compare them with some of the concepts underlying noncommutative geometry.

Title: Reduced products of UHF algebras under forcing axioms

Por • 25 mar, 2013 • Category: Crítica

If $A_n$ is a sequence of C*-algebras, then the C*-algebra $\prod A_n / \bigoplus A_n$ is called a reduced product. We prove, assuming Todorcevic’s Axiom and Martin’s Axiom, that every isomorphism between two reduced products of separable, unital UHF algebras must be definable in a strong sense. As a corollary we deduce that two such reduced products $\prod A_n / \bigoplus A_n$ and $\prod B_n / \bigoplus B_n$ are isomorphic if and only if, up to an almost-permutation of $\mathbb{N}$, $A_n$ is isomorphic to $B_n$.

Tomita-Takesaki Modular Theory vs. Quantum Information Theory

Por • 12 ene, 2013 • Category: Crítica

In this review article, we make an attempt to find out the relationship between separating and cyclic vectors in the theory of von Neumann algebra and entangled states in the theory of quantum information. The corresponding physical interpretation is presented as well.