On copies of $c_0$ in the bounded linear operator space

Juan Carlos Ferrando; J. M. Amigó

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Displaying similar documents to “On copies of $c_{0}$ in the bounded linear operator space”

On ultrapowers of Banach spaces of type $ℒ_{\infty}$

Antonio Avilés, Félix Cabello Sánchez, Jesús M. F. Castillo, Manuel González, Yolanda Moreno (2013)

Fundamenta Mathematicae

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We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain c₀ complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs have been infected by that statement. In particular we provide proofs for the following statements: (i) All M-spaces, in particular all C(K)-spaces, have ultrapowers isomorphic to ultrapowers of c₀, as also do all their complemented subspaces isomorphic...

Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures

Giovanni Emmanuele (1996)

Commentationes Mathematicae Universitatis Carolinae

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In the paper [5] L. Drewnowski and the author proved that if $X$ is a Banach space containing a copy of $c_{0}$ then $L_{1} (μ, X)$ is complemented in $c a b v (μ, X)$ and conjectured that the same result is true if $X$ is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if $μ$ is a finite measure and $X$ is a Banach lattice not containing copies of $c_{0}$ , then $L_{1} (μ, X)$ is complemented in $c a b v (μ, X)$ . Here, we show that the complementability of $L_{1} (μ, X)$ ...

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...

Projections from $L (X, Y)$ onto $K (X, Y)$

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

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Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let $X$ and $Y$ be Banach spaces such that $X$ is weakly compactly generated Asplund space and $X^{*}$ has the approximation property (respectively $Y$ is weakly compactly generated Asplund space and $Y^{*}$ has the approximation property). Suppose that $L (X, Y) \neq K (X, Y)$ and let $1 < λ < 2$ . Then $X$ (respectively $Y$ ) can be equivalently renormed so that any projection $P$ of $L (X, Y)$ onto $K (X, Y)$ has the sup-norm greater or equal to $λ$ . ...

Displaying similar documents to “On copies of c 0 in the bounded linear operator space”

On ultrapowers of Banach spaces of type ℒ ∞

Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures

The structure of Lindenstrauss-Pełczyński spaces

Projections from L ( X , Y ) onto K ( X , Y )

Displaying similar documents to “On copies of $c_{0}$ in the bounded linear operator space”

On ultrapowers of Banach spaces of type $ℒ_{\infty}$

Projections from $L (X, Y)$ onto $K (X, Y)$