The Poulsen simplex

Joram Lindenstrauss; Gunnar Olsen; Y. Sternfeld

Displaying similar documents to “The Poulsen simplex”

A note on the paper “The Poulsen Simplex” of Lindenstrauss, Olsen and Sternfeld

Wolfgang Lusky (1978)

Annales de l'institut Fourier

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It is proved that for any $f, g \in A (S)$ , where $S$ is the Poulsen simplex, so that $f, g$ and $1 - f$ , $1 - g$ are smooth points, there is a rotation of $A (S)$ carrying $f$ in $g$ .

A simplex with dense extreme points

Ebbe T. Poulsen (1961)

Annales de l'institut Fourier

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L’article décrit la construction (dans l’espace de Hilbert $l^{2}$ ) d’un simplexe (terminologie de Choquet) compact qui est la fermeture de l’ensemble de ses points extrémaux.

On the complemented subspaces of the Schreier spaces

I. Gasparis, D. Leung (2000)

Studia Mathematica

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It is shown that for every 1 ≤ ξ < ω, two subspaces of the Schreier space $X^{ξ}$ generated by subsequences $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ , respectively, of the natural Schauder basis $(e_{n}^{ξ})$ of $X^{ξ}$ are isomorphic if and only if $(e_{l_{n}}^{ξ})$ and $(e_{m_{n}}^{ξ})$ are equivalent. Further, $X^{ξ}$ admits a continuum of mutually incomparable complemented subspaces spanned by subsequences of $(e_{n}^{ξ})$ . It is also shown that there exists a complemented subspace spanned by a block basis of $(e_{n}^{ξ})$ , which is not isomorphic to a subspace generated by a subsequence of $(e_{n}^{ζ})$ ,...

On the representation of functions by orthogonal series in weighted $L^{p}$ spaces

M. Grigorian (1999)

Studia Mathematica

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It is proved that if $φ_{n}$ is a complete orthonormal system of bounded functions and ɛ>0, then there exists a measurable set E ⊂ [0,1] with measure |E|>1-ɛ, a measurable function μ(x), 0 < μ(x) ≤ 1, μ(x) ≡ 1 on E, and a series of the form $\sum_{k = 1}^{\infty} c_{k} φ_{k} (x)$ , where $c_{k} \in l_{q}$ for all q>2, with the following properties: 1. For any p ∈ [1,2) and $f \in L_{μ}^{p} [0, 1] = f : ʃ_{0}^{1} {| f (x) |}^{p} μ (x) d x < \infty$ there are numbers $ɛ_{k}$ , k=1,2,…, $ɛ_{k}$ = 1 or 0, such that $l i m_{n \to \infty} ʃ_{0}^{1} {| \sum_{k = 1}^{n} ɛ_{k} c_{k} φ_{k} (x) - f (x) |}^{p} μ (x) d x = 0 .$ 2. For every p ∈ [1,2) and $f \in L_{μ}^{p} [0, 1]$ there are a function $g \in L^{1} [0, 1]$ with g(x) = f(x) on E and numbers $δ_{k}$ , k=1,2,…, $δ_{k} = 1$ or 0,...

Inducing approximations homotopic to maps between inverse limits

J. Rogers (1973)

Fundamenta Mathematicae

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A lifting theorem for locally convex subspaces of $L_{0}$

R. Faber (1995)

Studia Mathematica

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We prove that for every closed locally convex subspace E of $L_{0}$ and for any continuous linear operator T from $L_{0}$ to $L_{0} / E$ there is a continuous linear operator S from $L_{0}$ to $L_{0}$ such that T = QS where Q is the quotient map from $L_{0}$ to $L_{0} / E$ .

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

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We investigate in a geometrical way the point sets of $ℝ$ obtained by the $β$ -numeration that are the $β$ -integers $ℤ_{β} \subset ℤ [β]$ where $β$ is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the $β$ -numeration, allowing to lift up the $β$ -integers to some points of the lattice $ℤ^{m}$ ( $m =$ degree of $β$ ) lying about the dominant eigenspace of the companion matrix of $β$ . When $β$ is in particular a Pisot number, this framework gives another proof of the fact...

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

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Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^{p} (ℝ)$ -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_{m} f (x) = p . v . \int k (x - y) m (x + y) f (y) d y$ where $k (x) = \sum_{j \in ℤ} 2^{j} φ_{j} (2^{j} x)$ for a family of functions ${φ_{j}}_{j \in ℤ}$ satisfying conditions (1.1)-(1.3) given below.