1,721,019 research outputs found
Renorming of ℓ1 and the fixed point property
No full textAbstractFor any k∈N, let Pk denote the natural projections on ℓ1. Let |||⋅||| be an equivalent norm of ℓ1 that satisfies all of the following four conditions:(1)There are α>4 and a positive (decreasing) sequence (αn) in (0,1) such that for any normalized block basis {fn} of (ℓ1,|||⋅|||) and x∈ℓ1 with Pk−1(x)=x and |||x|||<αk,lim supn→∞|||fn+x|||⩽1+|||x|||α.(2)There are two strictly decreasing sequences {βk} and {γk} withlimk→∞βk=0andlimk→∞γk=1 such that for any normalized block basis {fn} of (ℓ1,|||⋅|||) and x with (I−Pk)(x)=x,lim infn→∞|||fn+x|||⩾1−βk+γk−1|||x|||.(3)For any k∈N, ‖I−Pk‖=1.(4)The unit ball of (ℓ1,|||⋅|||) is σ(ℓ1,c0)-closed. In this article, we prove that the space (ℓ1,|||⋅|||) has the fixed point property for the nonexpansive mapping. This improves a previous result of the author
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
k-Uniform Rotundity of Lorentz–Orlicz Spaces
No full textAbstractIt is known that if an Orlicz function space isk-uniformly rotund for somek≥2, then it must be uniformly convex. In the paper, we show that a similar result holds in Lorentz–Orlicz function spaces
Extreme points of Banach lattices related to conditional expectations
No full textAbstractLet (X,F,μ) be a complete probability space, B a sub-σ-algebra, and Φ the probabilistic conditional expectation operator determined by B. Let K be the Banach lattice {f∈L1(X,F,μ):‖Φ(|f|)‖∞<∞} with the norm ‖f‖=‖Φ(|f|)‖∞. We prove the following theorems:(1)The closed unit ball of K contains an extreme point if and only if there is a localizing set E for B such that supp(Φ(χE))=X.(2)Suppose that there is n∈N such that f⩽nΦ(f) for all positive f in L∞(X,F,μ). Then K has the uniformly λ-property and every element f in the complex K with ‖f‖⩽1n is a convex combination of at most 2n extreme points in the closed unit ball of K
k-Uniform rotundity is equivalent to k-uniform convexity
No full textAbstractR. Geremia and F. Sullivan proved that 2-uniform rotundity is equivalent to 2-uniform convexity. This paper extends this result to k-uniformly rotund spaces
Generalized bi-circular projections
No full textAbstractRecall that a projection P on a complex Banach space X is a generalized bi-circular projection if P+λ(I−P) is a (surjective) isometry for some λ such that |λ|=1 and λ≠1. It is easy to see that every hermitian projection is generalized bi-circular. A generalized bi-circular projection is said to be nontrivial if it is not hermitian. Botelho and Jamison showed that a projection P on C([0,1]) is a nontrivial generalized bi-circular projection if and only if P−(I−P) is a surjective isometry. In this article, we prove that if P is a projection such that P+λ(I−P) is a (surjective) isometry for some λ, then either P is hermitian or λ is an nth unit root of unity. We also show that for any nth unit root λ of unity, there are a complex Banach space X and a nontrivial generalized bi-circular projection P on X such that P+λ(I−P) is an isometry
Remarks on linear selections for the metric projection
No full textAbstractThe aim of this paper is to give a characterization of the finite-dimensional subspaces of Lp, 1 ⩽ p < ∞, and C0(T) whose metric projections admit linear selections. The paper also gives a characterization of finite co-dimensional subspaces of l1 and c0 whose metric projections have linear selections
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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