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Results tagged with banach-spaces
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user 10583
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
7
votes
1
answer
361
views
Nonexpansive multi-valued maps in $\ell^2$
Let $C$ be a nonempty bounded closed convex subset, say the unit ball, of $\ell^2(\mathbb{N})$. Let $T: C\to 2^C$ be a map such that $T(x)$ is nonempty closed for each $x$, and that $$D(Tx,Ty)\le \|x- …
- 744
4
votes
1
answer
2k
views
Characterizations of a linear subspace associated with Fourier series
Let $c_0$ be the Banach space of doubly infinite sequences $$\lbrace
a_n: -\infty\lt n\lt \infty, \lim_{|n|\to \infty} a_n=0 \rbrace.$$ Let $T$ be the space of $2\pi$ periodic functions integrable …
- 744
2
votes
Accepted
Characterizations of a linear subspace associated with Fourier series
This is to summarize what were discussed in the comments, so the title will not be listed as unanswered.
The linear subspace $S$ of $c_0(\mathbb{Z})$ is equal to the convolution product of two copies …
- 744
1
vote
Variants of point fixed theorem
Let X be the predual of E. If the dual of every separable subspace of X is separable, then C contains a point that is fixed by EVERY weak* continuous affine isometry of C into C.
This is Theorem 2 in …
- 744