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

Sophie Grivaux; Jan Rychtář — 2006

Czechoslovak Mathematical Journal

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 $𝔸 (X)$ of biconjugates of bounded operators on $X$ : $𝔸 (X) = {T^{* *} T \in ℬ (X)}$ . 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 $ℓ_{1}$ and has property (u) of Pelczynski is simple.

Reversibility for diffusions via quasi-invarience

Omar Revasplata; Jan Rychtář; Byron Schmuland — 2007

Acta Universitatis Carolinae. Mathematica et Physica

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Invariant subspaces of X * * under the action of biconjugates

Reversibility for diffusions via quasi-invarience

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