Unconditional decompositions in subspaces of \(l_{2}(X)\) (Q1780508)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Unconditional decompositions in subspaces of \(l_{2}(X)\) |
scientific article; zbMATH DE number 2175438
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unconditional decompositions in subspaces of \(l_{2}(X)\) |
scientific article; zbMATH DE number 2175438 |
Statements
Unconditional decompositions in subspaces of \(l_{2}(X)\) (English)
0 references
13 June 2005
0 references
If a Banach space \(X\) is not isomorphic to a Hilbert space, then \(l_2(X)\) contains a subspace with an unconditional finite-dimensional decomposition (UFDD) which does not admit a UFDD with a uniform bound for the dimensions. If, moreover, \(X\) has finite cotype, then for every \(k >1\) there is a subspace of \(l_2(X)\) which has a \(k\)-dimensional UFDD, but does not possess a \((k-1)\)-dimensional UFDD.
0 references
Banach spaces
0 references
unconditional basis
0 references
unconditional decomposition
0 references
cotype
0 references
0 references
