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Results tagged with banach-spaces
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user 75
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
6
votes
Accepted
Operator on a Banach space
This is not necessarily true, and in fact you can get a counterexample where each $\lambda_i=0$. Consider $V=c_0$ and let $N_i=\sum_{j=0}^i j$ be the $i$th triangular number. Define $T:c_0\to c_0$ b …
- 31.2k
19
votes
Accepted
Description of $\big(\ell^\infty(\mathbb N)\big)^{\!*}$ via ultrafilters
Identify $\mathbb{N}$ with $\mathbb{Q}\cap[0,1]$ via a bijection, and consider the subspace $C([0,1])\subset\ell^\infty(\mathbb{N})$ of sequences which extend to a continuous function on $[0,1]$. Whe …
- 31.2k