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We study the connection between intersection properties of balls and the existence of large faces of the unit ball in Banach spaces. Hanner’s result that a real space has the 3.2 intersection property if an only if disjoint faces of the unit ball are contained in parallel hyperplanes is extended to infinite dimensional spaces. It is shown that the space of compact operators from a space $X$ to a space $Y$ has the 3.2 intersection property if and only if $X$ and $Y$ have the 3.2 intersection property and...

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.

Displaying 1 – 6 of 6

Idéaux d'opérateurs. Adjonction

Injektive Operatorenideale über der Gesamtheit aller Banachräume und ihre topologische Erzeugung

Inner M-ideals in Banach algebras.

Integral representation of additive transformations on L p spaces

Intersection properties of balls in spaces of compact operators

Invariant subspaces of X * * under the action of biconjugates

Currently displaying 1 – 6 of 6

Integral representation of additive transformations on $L_{p}$ spaces

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