I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: $\ex …

I have two mapping tori $A_{n}$={$f\in C([0,1], M_{n}(\mathbb{R}))\mid f(1)=\alpha_{1}(f(0))$}, $B_{n}$={$f\in C([0,1], M_{n}(\mathbb{R}))\mid f(1)=\alpha_{2}(f(0))$} where $\alpha …

It is known that an intertwining (or even approximately intertwining) diagram implies the isomorphism of the limit algebras. Under what conditions the converse holds?

Let $\mathbb{T}=[0,1]$ be identified with the circle $\{ e^{2 \pi it} : t \in [0,1] \}$, $\delta_0 \in M(\mathbb{T})$ be the Dirac measure at $0 \in \mathbb{T}$. Suppose $f \in L^1 …

"In this section, we deal with positive linear maps $\phi : A \rightarrow M$ between two unital C∗-algebra $A$ and $M$ with units denoted by $I$. In fact, we may assume that $A$ is …

EDIT: André Henriques has commented below that the correct separability condition is not weak-* separability as I have written below, but separability of the predual. This post c …

Hello, I need help determining whether the map I defined between two algebras is a well-defined homomorphism of $C^\ast$-algebras. I ran into this problem while trying to define a …

Let $M_n$ denote the $n$ by $n$ matrices. Consider the homomorphisms $$\phi_{n,kn}: M_n \rightarrow M_{kn}$$ which takes a matrix $A \in M_n$ to $A \otimes I_k \in M_{kn}.$ This gi …

Let A be a type $I$ factor on a Hilbert space H. Let $\varphi$ be a semi-finite normal weight on $A^{+}$ is it possible to say that then there exist Hilbert spaces $H_2 \subset H_1 …

Let $C(\mathbb{R};{U}(n))$ denote the topological group of continuous functions $\mathbb{R}\to {U}(n)$ with pointwise multiplication and compact-open topology. My question is: Are …

Tannaka-Krein duality shows how to recover a group $G$ from its category $\mathbf{Rep}(G)$ of finite-dimensional complex representations and the forgetful functor $F:\mathbf{Rep}(G …

A C*-algebra is nuclear if the algebraic tensor product $A\odot B$ ($B$ is any other C*-algebra) admits a unique C*-norm. This definition requires testing the condition for nuclear …

We know that amenability of countable discrete group $\Gamma$ has many equivalent characterizations. In particular, there are two: a) there is a sequence of finitely supported posi …

While analyzing convergence speed of stochastic-gradient methods for convex optimization problems, Recht et al (2011) posed a tantalizing conjecture. It seems quite tricky, so afte …

Let X be a Banach space. $B(X)$ is the algebra of all bounded linear operators on X. $\phi: B(X)\rightarrow B(X)$ is a isomoprphisn, $\varphi: B(X)\rightarrow B(X)$ is a isomorphis …