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Results tagged with banach-spaces
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user 54609
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
1
vote
Subspaces of $l_{1}$ are not Lipschitz complemented in $l_{1}$
This is not an answer, just a related question: In the particular case when $U$ is complemented in its bidual, you have that $U$ is Lipschitz complemented in $\ell_1$ if and only if $U$ is complemente …
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4
votes
Accepted
Corson-Lindenstrauss : Weakly compact sets as intersection of finite unions of cells
Let $x_n=-\frac{\sum_{k=1}^n e_k}{n}$. Then $\|e_i-x_n\|^2=\frac{n+3}{n}$ if $i \leq n$ and $\|e_i-x_n\|^2=\frac{n+1}{n}$ if $i>n$. So your set is the intersection of the sets $B(x_n,\sqrt{\frac{n+1}{ …
- 716
4
votes
relation between of uniformly rotund in every direction and uniformly rotund and locally uni...
First, the fact that UR implies URED is obvious (the definition of UR requires less from the sequences $(x_n)$, $(y_n)$ in order to conclude the convergence $\|x_n-y_n\|\to 0$.)
Second, the notions L …
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