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Results tagged with open-problems
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user 1162
If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
6
votes
0
answers
290
views
What is the status of the subadditivity problem for analytic capacity?
Hi,
Here is another question that concerns analytic capacity. For a compact set $K$ in the plane, define the analytic capacity of $K$ by
$$\gamma(K):=\sup|f'(\infty)|,$$
where the supremum is taken o …
- 2,154
78
votes
Not especially famous, long-open problems which anyone can understand
I always enjoyed telling people about the Inscribed square problem :
Does every (Jordan) curve in the plane contain all four vertices of
some square?
Update: Here is a variation due to Helge Tverbe …
5
votes
In a Banach algebra, do ab and ba have almost the same exponential spectrum?
Bonjour Yemon,
Oui, c'est un problème proposé par TJR dans le cadre d'un projet de recherche d'été CRSNG.
It is indeed a very subtle question, I thought it might interest some people here. This probl …
- 2,154
21
votes
2
answers
2k
views
In a Banach algebra, do ab and ba have almost the same exponential spectrum?
Let $A$ be a complex Banach algebra with identity 1. Define the exponential spectrum $e(x)$ of an element $x\in A$ by $$e(x)= \{\lambda\in\mathbb{C}: x-\lambda1 \notin G_1(A)\},$$ where $G_1(A)$ is th …
- 2,154