Tagged Questions
3
votes
2answers
96 views
Geometric Sums in Banach Algebra
Let $E$ be a Banach algebra, and $v\in E$, so that $||v|| < 1$. So the geometric series $w = \sum_{k=0}^\infty v^k$ converges in the norm, that part I understand.
I can show that $||w|| \le ...
6
votes
1answer
199 views
When is the weighted space $\ell^p(\mathbb{Z},\omega)$ a Banach algebra ($p>1$)?
Let $\omega:\mathbb{Z}\to (0,\infty)$ and let $1\leq p<\infty$. Consider the space $\ell^p(\mathbb{Z},\omega)$ of complex valued sequences $f=(a_n)_{n \in \mathbb{Z}}$ such that
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