All Questions
7 questions
4
votes
1
answer
332
views
Support projection vs closed support projection of a normal state in enveloping von Neumann algebra
I preface this by saying that I am fairly new to the enveloping von Neumann algebra scene, so there may be some gaps in my understanding.
Given a $C^*$-algebra $A$ and a state $\phi$ on $A$, one may ...
- 135
2
votes
0
answers
89
views
Computing norms of polynomials of operator in Hilbert space and generalized von Neumann inequality
Let $T$ be an operator $l^2({\mathbb{Z}_{\geq 0}}) \to l^2({\mathbb{Z}_{\geq 0}})$, $e_n \mapsto \sqrt{1 - q^{2(n+1)}}e_{n+1} $, where $0<q<1$. I want to compute $\|f(T,T^{*}) \|$ (operator ...
- 161
2
votes
1
answer
97
views
Approximation of unity by projectors
Let $A$ be a $\sigma$-unital $C^*$-algebra and $A_s:=A\otimes K$ its stabilization (where $K$ is the algebra of compact operators on a separable Hilbert space). Is it true that there exist an ...
- 18.7k
6
votes
2
answers
690
views
Can $C^*$-algebra of continuous functions on $R^n$ ($S^n$) be characterized alternatively?
Dictionary between algebra and geometry is somewhat one of the main concepts in modern mathematics. So commutative $C^*$ algebras are one-to-one with locally compact Hausdorff spaces.
So it is ...
- 356
4
votes
0
answers
207
views
Extending Akemann's Non-Commutative Urysohn Lemma
Assume $A$ is a C*-algebra and $p,q\in A^{**}$ are compact projections.
Can we always find $a,b\in A^1_+$ with $p\leq a$, $q\leq b$ and $||pq||=||ab||$?
Note if $||pq||=1$ this is immediate, while ...
- 1,307
3
votes
0
answers
146
views
Closed containment of open projections in C*-algebras
For a C*-algebra $A$ and open projections $p,q\in A^{**}$, consider the following statements.
$\overline{p}\leq q$
$p\leq q$ and there exists open $r\in A^{**}$ with $rp=0$ and $r\vee q=1$
$p\leq q$ ...
- 1,307
4
votes
1
answer
312
views
A question on $Z^{*}$ algebras
A $Z^{*}$ algebra is a $C^{*}$ algebra which satisfies each of the following equivalent conditions:
All elements of $A$ are left zero divisor.
All elements are right zero divisor.
All elements are ...
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