A disjointness property of $l^n_p$ sequences in $L_p$

G. Schechtman

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Operators into $L_{p}$ which factor through $l_{p}$

W. B. Johnson (1979-1980)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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A simple formula showing L¹ is a maximal overspace for two-dimensional real spaces

B. L. Chalmers, F. T. Metcalf (1992)

Annales Polonici Mathematici

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It follows easily from a result of Lindenstrauss that, for any real twodimensional subspace v of L¹, the relative projection constant λ(v;L¹) of v equals its (absolute) projection constant $λ (v) = s u p_{X} λ (v; X)$ . The purpose of this paper is to recapture this result by exhibiting a simple formula for a subspace V contained in $L^{\infty} (ν)$ and isometric to v and a projection $P_{\infty}$ from C ⊕ V onto V such that $∥ P_{\infty} ∥ = ∥ P ₁ ∥$ , where P₁ is a minimal projection from L¹(ν) onto v. Specifically, if $P ₁ = \sum_{i = 1}^{2} U_{i} \otimes v_{i}$ , then $P_{\infty} = \sum_{i = 1}^{2} u_{i} \otimes V_{i}$ , where $d V_{i} = 2 v_{i} d ν$ and $d U_{i} = - 2 u_{i} d ν$ .

Semivariation in $L^{p}$ -spaces

Brian Jefferies, Susumu Okada (2005)

Commentationes Mathematicae Universitatis Carolinae

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Suppose that $X$ and $Y$ are Banach spaces and that the Banach space $X {\hat{\otimes}}_{τ} Y$ is their complete tensor product with respect to some tensor product topology $τ$ . A uniformly bounded $X$ -valued function need not be integrable in $X {\hat{\otimes}}_{τ} Y$ with respect to a $Y$ -valued measure, unless, say, $X$ and $Y$ are Hilbert spaces and $τ$ is the Hilbert space tensor product topology, in which case Grothendieck’s theorem may be applied. In this paper, we take an index $1 \leq p < \infty$ and suppose that $X$ and $Y$ are $L^{p}$ -spaces with $τ_{p}$ the associated...

A zero-two theorem for a certain class of positive contractions in finite dimensional $L^{P}$ -spaces $(1 ⩽ p < + \infty)$

R. Zaharopol (1984)

Annales scientifiques de l'Université de Clermont-Ferrand 2. Série Probabilités et applications

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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...

Second derivatives of norms and contractive complementation in vector-valued spaces

Bas Lemmens, Beata Randrianantoanina, Onno van Gaans (2007)

Studia Mathematica

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We consider 1-complemented subspaces (ranges of contractive projections) of vector-valued spaces $ℓ_{p} (X)$ , where X is a Banach space with a 1-unconditional basis and p ∈ (1,2) ∪ (2,∞). If the norm of X is twice continuously differentiable and satisfies certain conditions connecting the norm and the notion of disjointness with respect to the basis, then we prove that every 1-complemented subspace of $ℓ_{p} (X)$ admits a basis of mutually disjoint elements. Moreover, we show that every contractive projection...

A note on copies of $c_{0}$ in spaces of weak* measurable functions

Juan Carlos Ferrando (2000)

Commentationes Mathematicae Universitatis Carolinae

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If $(Ω, Σ, μ)$ is a finite measure space and $X$ a Banach space, in this note we show that $L_{w^{*}}^{1} (μ, X^{*})$ , the Banach space of all classes of weak* equivalent $X^{*}$ -valued weak* measurable functions $f$ defined on $Ω$ such that $∥ f (ω) ∥ \leq g (ω)$ a.e. for some $g \in L_{1} (μ)$ equipped with its usual norm, contains a copy of $c_{0}$ if and only if $X^{*}$ contains a copy of $c_{0}$ .

Structure of Rademacher subspaces in Cesàro type spaces

Sergey V. Astashkin, Lech Maligranda (2015)

Studia Mathematica

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The structure of the closed linear span of the Rademacher functions in the Cesàro space $C e s_{\infty}$ is investigated. It is shown that every infinite-dimensional subspace of either is isomorphic to l₂ and uncomplemented in $C e s_{\infty}$ , or contains a subspace isomorphic to c₀ and complemented in . The situation is rather different in the p-convexification of $C e s_{\infty}$ if 1 < p < ∞.

Displaying similar documents to “A disjointness property of l p n sequences in L p ”

Displaying similar documents to “A disjointness property of $l_{p}^{n}$ sequences in $L_{p}$ ”