Displaying similar documents to “A note on a theorem of Klee”

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies ξ on a fixed infinite dimensional vector space E such that ( E , ξ ) has not the Hahn-Banach extension property but the topological dual ( E , ξ ) ' separates points of E from zero is given.

A note on Banach spaces with ℓ 1 -saturated duals

Denny H. Leung (1996)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that there exists a Banach space with an unconditional basis which is not c 0 -saturated, but whose dual is ℓ 1 -saturated.

Invariant subspaces of X * * under the action of biconjugates

Sophie Grivaux, Jan Rychtář (2006)

Czechoslovak Mathematical Journal

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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 ∈ 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.