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Results tagged with banach-algebras
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user 1162
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
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
2
votes
$\mathcal P(K)=\mathcal R(K)$ iff $\Bbb C\backslash K$ is connected
Perhaps a more elementary proof is the following :
Assume $\mathbb{C} \setminus K$ is disconnected. Let $V$ be a bounded component of $\mathbb{C} \setminus K$, and let $w \in V$. Let us show that the …
- 2,154