Invariant subspaces of $X^{**}$ under the action of biconjugates

Title:

Invariant subspaces of $X^{**}$ under the action of biconjugates

Creator:

Grivaux, Sophie and Rychtář, Jan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a75fe6ee-237d-48a2-ba35-86f445ba4d6e
uuid:a75fe6ee-237d-48a2-ba35-86f445ba4d6e

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

Type:

model:article and TEXT

Format:

bez média and svazek

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

61-77

Source:

Czechoslovak Mathematical Journal | 2006 Volume:56 | Number:1

Harvested from:

CDK

Metadata only:

false