| Title:
|
Invariant subspaces of $X^{**}$ under the action of biconjugates (English) |
| Author:
|
Grivaux, Sophie |
| Author:
|
Rychtář, Jan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
61-77 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study conditions on an infinite dimensional separable Banach space $X$ implying that $X$ is the only non-trivial invariant subspace of $X^{**}$ under the action of the algebra $\mathbb{A}(X)$ of biconjugates of bounded operators on $X$: $\mathbb{A}(X)=\lbrace T^{**}\: T \in \mathcal {B}(X)\rbrace $. Such a space is called simple. We characterize simple spaces among spaces which contain an isomorphic copy of $c_{0}$, and show in particular that any space which does not contain $\ell _1$ and has property (u) of Pelczynski is simple. (English) |
| Keyword:
|
algebras of operators with only one non-trivial invariant subspace |
| Keyword:
|
invariant subspaces under the action of the algebra of biconjugates operators |
| Keyword:
|
transitivity |
| Keyword:
|
property (u) of Pelczynski |
| MSC:
|
46B10 |
| MSC:
|
46B25 |
| MSC:
|
46B99 |
| MSC:
|
47A15 |
| MSC:
|
47L05 |
| idZBL:
|
Zbl 1164.47302 |
| idMR:
|
MR2206287 |
| . |
| Date available:
|
2009-09-24T11:31:35Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128054 |
| . |
| Reference:
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