0
votes
1answer
165 views

Find a special element in group algebra

Let $$G=\langle x, y, z\mid xyx^{-1}=zy, xzx^{-1}=z, yz=zy\rangle,$$ denote $l^1(G)^{\times}$ to be the set of units in $l^1(G)$, which we have considered as a ring with multiplication defined by the ...
3
votes
1answer
251 views

Metrics and completions on the direct limit of matrices of all sizes over arbitrary fields

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 gives a sensible way ...
1
vote
0answers
205 views

How to find the tensor product of modules that we don't know a basis for them?

Hi I know how to calculate some easy tensor products like $\mathbb{Z}/m\mathbb{Z} \otimes_{\mathbb{Z}} \mathbb{Z}/n\mathbb{Z}\cong_{\mathbb{Z}} \mathbb{Z}/(m,n)\mathbb{Z} $ or $F[X] \otimes_{F} F[Y] ...
1
vote
0answers
195 views

bivariate polynomial

Hello, Let $p(x,y) = \sum_{m=1}^M\sum_{n=1}^N a_{m,n}x^{m-1}y^{n-1}$ be a bivariate polynomial where $\{a_{m,n}\}$ are complex. If $(x_k, y_k), k=1,2,\cdots, MN-1$ are roots of $p(x,y)=0$ where ...
3
votes
0answers
157 views

Is the construction of ring C*-algebra functorial?

Cunz and Li defined defined C*-algebras for arbitrary rings with of course some condition. One can look at their article (http://arxiv.org/abs/0905.4861). My question: is the construction functorial? ...
4
votes
2answers
398 views

rank of fin gen projective modules over C* algebras

Apologies - a better explanation than I started with - thanks to people for helping. It is obvious that there are many bad cases for rank - the problem is are there a reasonable number of good cases? ...
0
votes
1answer
159 views

Laurent series with analytic coefficients

Let $A=H(D(0,1))$ the ring of holomorphic functions on the open unity disc. I consider the function $f$: $$f (t)=\sum f_{i}t^{i} \in A[[t]]$$ I suppose that the $t$-adic valuation of it is less or ...
2
votes
1answer
186 views

Subalgebras of $B(E)$

Let me fix an infinite-dimensional (complex) Banach space $E$. There is a cute result of Bracic and Kuzma which says that every maximal abelian subalgebra of $\mathscr{B}(E)$, the algebra of bounded ...
5
votes
1answer
225 views

Is there a tropical analogue of a reproducing kernel Hilbert space?

In classical functional analysis, one can construct a reproducing kernel Hilbert space by starting with a positive definite kernel, say $K: [0,1]\times [0,1] \rightarrow \mathbb{R}$. One then creates ...
4
votes
0answers
276 views

When quotient of a $k$-algebra by any maximal ideal is $k$?

Let $k$ be a valued field. Is there a special term for commutative (Banach) $k$-algebras, who's quotient by any maximal ideal is $k$? Is it possible, given a commutative (Banach) $k$-algebra, to check ...
3
votes
1answer
400 views

Are all quantum cellular automata invertible & representable?

A little background: As far as I know there is no standard definition of a quantum cellular automaton in the literature. Different authors use different definitions. Here I propose my own definition ...
0
votes
2answers
336 views

Commutative *-subrings of the noncommutative C*-algebra $B(l^2)$

A $\star$-ring is a ring with an involutive anti-automorphism. The simplest example of a noncommutative $\star$-ring is perhaps $B(l^2)$, the ring of bounded linear functions on the sequence space ...
2
votes
1answer
463 views

Is a polynomial positive on the sphere a sum of squares of spherical harmonic polynomials?

Let $p\in {\mathbb{R}}[x_1,\ldots, x_n]$ be a homogenous polynomial of even degree $2d$. If $p$ is positive on the unit sphere $S\subset {\mathbb{R}}^n$, then does there exist some $m>0$ and ...
2
votes
0answers
430 views

Eigenvector of infinite matrix

I consider the system of reaction-diffusion PDEs in a ball with Robin boundary condition. It is a Steklov eigenvalue problem (see G Auchmuty (2004) "Steklov eigenproblems and the representation of ...
5
votes
0answers
275 views

Is there an idempotent measure on the free LD system?

This is a follow up question to MO question "Idempotent measures on the free binary system?". Let $(A,*)$ be the free binary operation on one generator which satisfies the left self distributive law: ...
7
votes
2answers
726 views

What is the smallest $C^*$-algebra containing the “standard” pseudodifferential operators?

Is $\Psi^0(\mathbb{R})$ (pseudodifferential operators with symbols obeying $ |\partial^\alpha_x \partial^\beta_\xi a(x,\xi)| \leq C_{\alpha,\beta} (1+|\xi|)^{-|\beta|} $ ) a $C^*$-algebra? In other ...
1
vote
1answer
349 views

Intersection of ideals in C*-algebra or even rings in general

Dear all, here is a question that has been bothering me. It goes without saying that I would appreciate any help in answering it. Let {I_k} be a countable sequence of two sided closed ideals in a ...