Ergodic theory | Von Neumann algebras | Representation theory of groups | Theorems in representation theory | Theorems in functional analysis
In mathematics, a commutation theorem for traces explicitly identifies the commutant of a specific von Neumann algebra acting on a Hilbert space in the presence of a trace. The first such result was proved by Francis Joseph Murray and John von Neumann in the 1930s and applies to the von Neumann algebra generated by a discrete group or by the dynamical system associated with a measurable transformation preserving a probability measure. Another important application is in the theory of unitary representations of unimodular locally compact groups, where the theory has been applied to the regular representation and other closely related representations. In particular this framework led to an abstract version of the Plancherel theorem for unimodular locally compact groups due to Irving Segal and Forrest Stinespring and an abstract Plancherel theorem for spherical functions associated with a Gelfand pair due to Roger Godement. Their work was put in final form in the 1950s by Jacques Dixmier as part of the theory of Hilbert algebras. It was not until the late 1960s, prompted partly by results in algebraic quantum field theory and quantum statistical mechanics due to the school of Rudolf Haag, that the more general non-tracial Tomita–Takesaki theory was developed, heralding a new era in the theory of von Neumann algebras. (Wikipedia).
Trace of an Operator and of a Matrix
Trace of an operator defined to be the sum of the eigenvalues (or of the eigenvalues of the complexification), repeated according to multiplicity. Trace of a matrix defined to be the sum of the squares of the diagonal enties. The connection between these two notions of trace.
From playlist Linear Algebra Done Right
Ex: Find the Trace and Determinant of a 3x3 Matrix Using Eigenvalues
This video explains how to determine the trace and determinant of a 3x3 matrix using eigenvalues. http://mathispower4u.com
From playlist Eigenvalues and Eigenvectors
Use Traces of a Surface to Select the Equation of the Surface (Ex1)
This video explains how to determine the traces of function of two variables and then match given traces to the correct function. http://mathispower4u.com
From playlist Functions of Several Variables
Matrix Theory: Let A be an nxn matrix with complex entries. We show that the commutant of A has dimension greater than or equal to n. The key step is to show the result for the Jordan canonical form of A.
From playlist Matrix Theory
Use Traces of a Surface to Select the Equation of the Surface (Ex 2)
This video explains how to determine the traces of function of two variables and then match given traces to the correct function. http://mathispower4u.com
From playlist Functions of Several Variables
How do you find discontinuities?
In this video we talk about how to find discontinuities in a function. 0:02 How do you find the discontinuities when you have a picture of the graph of the function? // You need to look for any point where there’s any kind of hole, break, jump, asymptote, or endpoint in the graph. These w
From playlist Popular Questions
Ex: Limit of a Function of Two Variables (Not Origin - DNE)
This video explains how to find a limit of a function of two variables. Site: http://mathispower4u.com
From playlist Limits of Functions of Two Variables
Linear Algebra 17f: Easy Eigenvalues - The Determinant
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Determine the points of inflections with trig
👉 Learn how to find the points of inflection of a function given the equation or the graph of the function. The points of inflection of a function are the points where the graph of the function changes its concavity. The points of inflection can be found from the equation of a function by
From playlist Find the Points of Inflection of a Function
8ECM Invited Lecture: Stuart White
From playlist 8ECM Invited Lectures
In this video, we give an important motivation for studying Topological Cyclic Homology, so called "trace methods". Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://w
From playlist Topological Cyclic Homology
Gabriele Vezzosi - Applications of non-commutative algebraic geometry to arithmetic geometry
Abstract: We will briefly recall the general philosophy of non-commutative (and derived) algebraic geometry in order to establish a precise link between dg-derived category of singularities of Landau-Ginzburg models and vanishing cohomology, over an arbitrary henselian trait. We will then
From playlist Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday
Cyril Houdayer: Noncommutative ergodic theory of lattices in higher rank simple algebraic groups
Talk by Cyril Houdayer in the Global Noncommutative Geometry Seminar (Americas) on March 18, 2022. https://globalncgseminar.org/talks/tba-28/
From playlist Global Noncommutative Geometry Seminar (Americas)
Matrix trace inequalities for quantum entropy - M. Berta - Main Conference - CEB T3 2017
Mario Berta (Imperial) / 11.12.2017 Title: Matrix trace inequalities for quantum entropy Abstract: I will present multivariate trace inequalities that extend the Golden-Thompson and Araki-Lieb-Thirring inequalities as well as some logarithmic trace inequalities to arbitrarily many matric
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Distributional symmetries and non commutative (...) - C. Male - Workshop 2 - CEB T3 2017
Camille Male / 26.10.17 Distributional symmetries and non commutative notions of independence The properties of the limiting non commutative distribution of random matrices can be usually understood thanks to the symmetry of the model, e.g. Voiculescu's asymptotic free independence occur
From playlist 2017 - T3 - Analysis in Quantum Information Theory - CEB Trimester
Amine Marrakchi - Le problème du bicentralisateur de Connes
À la fin des années 1970, Connes formula une conjecture portant sur les facteurs de type III1 connue sous le nom de "problème du bicentralisateur" et montra qu'une solution positive à ce problème permettrait de prouver l'unicité du facteur moyennable de type III1. Cette conjecture de Conne
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
Learn how to find the points of inflection for an equation
👉 Learn how to find the points of inflection of a function given the equation or the graph of the function. The points of inflection of a function are the points where the graph of the function changes its concavity. The points of inflection can be found from the equation of a function by
From playlist Find the Points of Inflection of a Function