MathOverflow

Given a $C^*$ algebra $A$ with a fixed (left) representation on a given Hilbert space $H$, is there any way to see if a state $\phi:A\to\mathbb{C}$ is a vector state, i.e. if there is a $v\in H$ so that $\phi(a)=\big<\overline{v},a.v\big>$. ...

Ref: A claim on wrapping 3D solids with a sheet of paper
A sheet of paper (a polygonal region that can be folded or wrinkled at will but not stretched or torn) wraps a solid if we can fold the paper such that any path to any point on the surface of the solid from any far away point in space will have to cut...

Background. A friend and I who work in the representation theory of $p$-adic groups are trying, for culture, to understand some basic ideas from the relative Langlands program of Sakellaridis and Venkatesh. Without going too much into the details of...

Assume $\Gamma$ is an infinite set composed of terms (of finite length), and $A$ is a term (of finite length). For example, $\Gamma=\{x,y\sqcup z,x_1,x_2,x_3,\cdots\}$, $A=(x\sqcap y)\sqcup(x\sqcap z)$. Obviously, $\mathop⨅\Gamma\le A$ holds in any of...