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Results tagged with banach-spaces
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user 61785
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
5
votes
Set of w*-continuous operators closed for the weak* topology or not?
The answer is no. I know that for some people here, saying "It's false for $X = \ell^1$" would be a good enough hint, but I also know that this question originated on Math StackExchange, so I've inclu …
- 3,768
5
votes
Duality between Banach spaces and compact convex spaces
Judging by what you say in the question, I think you are referring to what Świrszcz called "Saks spaces" in this article:
Monadic functors and convexity, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astro …
- 3,768
10
votes
Accepted
Banach space with uncountable basis
I will pull together the comments into a community wiki answer with some of my own remarks so that the question isn't left on the unanswered questions list.
If you're willing to accept that it is cons …
7
votes
Accepted
Equivalence of σ-convex hull and closed convex hull
Wlod AA gave a good counterexample for the case when $K$ is not required to be compact, here I give a counterexample $K$ compact, first in a locally convex space, and then for a(n infinite-dimensional …
- 3,768
3
votes
Is the space of Radon measures a Polish space or at least separable?
The other answers very adequately explain why the norm topology is not Polish except for trivial cases, so this answer is about the weak-* topology. Also, most results in the literature are about the …
- 3,768