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Results tagged with banach-spaces
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user 26674
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
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
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