Displaying similar documents to “Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures”

On ultrapowers of Banach spaces of type ℒ ∞

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...

Banach spaces widely complemented in each other

Elói Medina Galego (2013)

Colloquium Mathematicae

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Suppose that X and Y are Banach spaces that embed complementably into each other. Are X and Y necessarily isomorphic? In this generality, the answer is no, as proved by W. T. Gowers in 1996. However, if X contains a complemented copy of its square X², then X is isomorphic to Y whenever there exists p ∈ ℕ such that X p can be decomposed into a direct sum of X p - 1 and Y. Motivated by this fact, we introduce the concept of (p,q,r) widely complemented subspaces in Banach spaces, where p,q and...

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.

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...

On complemented copies of c₀(ω₁) in C(Kⁿ) spaces

Leandro Candido, Piotr Koszmider (2016)

Studia Mathematica

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Given a compact Hausdorff space K we consider the Banach space of real continuous functions C(Kⁿ) or equivalently the n-fold injective tensor product ⊗ ̂ ε n C ( K ) or the Banach space of vector valued continuous functions C(K,C(K,C(K...,C(K)...). We address the question of the existence of complemented copies of c₀(ω₁) in ⊗ ̂ ε n C ( K ) under the hypothesis that C(K) contains such a copy. This is related to the results of E. Saab and P. Saab that X ⊗ ̂ ε Y contains a complemented copy of c₀ if one of the infinite-dimensional...

Isomorphic and isometric copies of ℓ ∞ ( Γ ) in duals of Banach spaces and Banach lattices

Marek Wójtowicz (2006)

Commentationes Mathematicae Universitatis Carolinae

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Let X and E be a Banach space and a real Banach lattice, respectively, and let Γ denote an infinite set. We give concise proofs of the following results: (1) The dual space X * contains an isometric copy of c 0 iff X * contains an isometric copy of ℓ ∞ , and (2) E * contains a lattice-isometric copy of c 0 ( Γ ) iff E * contains a lattice-isometric copy of ℓ ∞ ( Γ ) .