A note on Banach spaces with $\ell ^1$-saturated duals

Denny H. Leung

Displaying similar documents to “A note on Banach spaces with $ℓ^{1}$ -saturated duals”

On copies of $c_{0}$ in the bounded linear operator space

Juan Carlos Ferrando, J. M. Amigó (2000)

Czechoslovak Mathematical Journal

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In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $ℒ (X, Y)$ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.

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...

$w^{*}$ -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

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We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $ℒ (X, Y)$ is not reflexive for reflexive $X$ and $Y$ then $ℒ (X_{1}, Y)$ is is not reflexive for some $X_{1} \subset X$ , $X_{1}$ having a basis.

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 $L_{1} (μ, X)$ ...

Displaying similar documents to “A note on Banach spaces with ℓ 1 -saturated duals”

On copies of c 0 in the bounded linear operator space

On ultrapowers of Banach spaces of type ℒ ∞

w * -basic sequences and reflexivity of Banach spaces

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

Displaying similar documents to “A note on Banach spaces with $ℓ^{1}$ -saturated duals”

On copies of $c_{0}$ in the bounded linear operator space

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

$w^{*}$ -basic sequences and reflexivity of Banach spaces