1. Invariant subspaces of $X^{**}$ under the action of biconjugates
- Creator:
- Grivaux, Sophie and Rychtář, Jan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- algebras of operators with only one non-trivial invariant subspace, invariant subspaces under the action of the algebra of biconjugates operators, transitivity, and property (u) of Pelczynski
- Language:
- English
- Description:
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public