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Results tagged with fa.functional-analysis
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user 26674
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
1
vote
Which topology for compactness and continuity?
A slightly more classical answer than Kieth's answer.
The set of non-decreasing (monotone) functions (equivalence classes) $M$ of functions from $[0,1]$ to $[0,1]$ is norm-compact in the Banach spac …
- 900
3
votes
1
answer
387
views
Continuity of lattice operations in Banach lattices
Let $L$ be a Dedekind-complete Banach lattice. Let $\mathcal{B}$ be the family of nonempty norm-compact subsets of $L$ that are bounded from below. Endow $\mathcal{B}$ with the topology induced by th …
- 900
8
votes
1
answer
878
views
Certain compact subset of $L_1$
Let $(\Omega,\Sigma, \mu)$ be a probability measure and $X$ a Banach space. I am interested in subsets $F\subseteq L_\infty (\mu,X)$ that satisfy these two compactness conditions:
$F$ is a norm-com …
- 900
3
votes
Accepted
Certain compact subset of $L_1$
The answer is that (1) and (2) implies $\star$ (this resolves a nice problem in a game theory paper I'm working on though the final unresolved problem has to do with decomposable Banach spaces, which …
- 900
2
votes
When is a sequentially closed cone, closed?
In ordered vector spaces the question is restated as follows:
When does the Archimidean property imply that the positive cone of an ordered vector space is closed? So that should help in your search. …
- 900
6
votes
Banach lattice subspace of $C([0,1])$ not a sublattice
Aside from examples there is a nice and very useful characterizations due to Mayajima http://hmj2.math.sci.hokudai.ac.jp/359/ of lattice subspaces that need not be sublattices. It is of considerable i …
- 900