525 research outputs found
Set-valued Brownian motion
No full textBrownian motions, martingales, and Wiener processes are introduced and
studied for set valued functions taking values in the subfamily of compact convex
subsets of arbitrary Banach spaces X. The present paper is an application of the paper
(Labuschagne et al. in Quaest Math 30(3):285–308, 2007) in which an embedding
result is obtained which considers also the ordered structure of the family of compact convex subsets of a Banach space X and of Grobler and Labuschagne (J Math Anal
Appl 423(1):797–819, 2015; J Math Anal Appl 423(1):820–833, 2015) in which these
processes are considered in f-algebras.Moreover, in the space of continuous functions
defined on a Stonian space, a direct Levy’s result follows
A note on the Banach space of preregular maps
No full textThe aim of this paper is to give simple proofs for Jeurnink's characterizations of preregular maps in terms of Θ-maps acting between Banach lattices. For Banach lattices E and F, we achieve our goal by considering the space Lβ(E, F) of all those linear maps T: E → F for which there exists a constant K such that {double pipe}Vn i=1 {pipe}Txi{pipe} ≤ K {double pipe}Vn i=1{pipe}xi for all finite sequences x1, ..., xn e{open}E. We show that, if Lβ(E; F), and the spaces L Θ (E; F) of Θ -map and Lpr(E; F) of preregular maps are respectively endowed with their canonical norms, then they are identical Banach space
On spaces of Bochner and Pettis integrable functions and their set-valued counterparts
No full textThe aim of this paper is to give a brief summary of the Pettis and Bochner integrals, how they are related, how they are generalized to the set-valued setting and the canonical Banach spaces of bounded maps between Banach spaces that they generate. The main tool that we use to relate the Banach space-valued case to the set-valued case, is the R ̊adstr ̈om embedding theorem
On set-valued cone absolutely summing maps
No full textSpaces of cone absolutely summing maps are generalizations of Bochner spaces L(p)(mu, Y), where (Omega, Sigma, mu) is some measure space, 1 <= p < infinity and Y is a Banach space. The Hiai-Umegaki space L(1)[Sigma, cbf(X)] of integrably bounded functions F : Omega -> cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L(1)(mu, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of L(1)[Sigma, cbf(X)], and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We also describe these set-valued cone absolutely summing maps as those that map order-Pettis integrable functions to integrably bounded set-valued function
Quadratic Variation of Martingales in Riesz Spaces
No full textWe derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austin’s sample function theorem, on convergence of the quadratic variation processes of martingale
Weighted noncommutative Banach function spaces
No full textWe review the concept of a weighted noncommutative Banach function space. This concept constitutes a generalisation of the by now well-known theory of noncommutative Banach function spaces associated with a semifinite von Neumann algebra. In this review we remind the reader of the quantum statistical problem which gave birth to this concept, we investigate the extent to which a weighted theory of measurable operators agrees with the standard theory, we explore competing methods for defining such spaces, before finally describing the monotone interpolation theory of such space
On the uniform density of C(X) ⊗ C(Y) in C(X × Y)
No full textAbstractWe prove that if X and Y are compact Hausdorff spaces, then every f ∈ C(X × Y)+, i.e. f(x, y) ≥ 0 for all (x, y) ∈ X × Y, can be approximated uniformly from below and above by elements of the form ∑i=1nfigi, where fi ∈ C(X)+ and gi ∈ C(Y)+ for i = 1, 2, …, n. The proof uses only elementary topology. We use this result, in conjuction with Kakutani's M-spaces representation theorem, to obtain an alternative proof for a known property of Fremlin's Riesz space tensor product of Archimedean Riesz spaces
On vector-valued characters for noncommutative function algebras
No full textLet A be a closed subalgebra of a C∗-algebra, that is a norm-closed algebra of Hilbert space operators. We generalize to such operator algebras several key theorems and concepts from the theory of classical function algebras. In particular we consider several problems that arise when generalizing classical function algebra results involving characters (nontrivial homomorphisms from the algebra into the scalars). For example, the Jensen inequality, the related Bishop–Ito–Schreiber theorem, and the theory of Gleason parts. Inspired by Arveson’s work on noncommutative Hardy spaces, we replace characters (classical function algebra case) by D-characters; certain completely contractive homomorphisms Φ:A→D, where D is a C∗-subalgebra of A. Using Brown’s measure and a potential theoretic balayage argument we prove a partial noncommutative Jensen inequality appropriate for C∗-algebras with a tracial state. We also show that this Jensen inequality characterizes D-characters among the module maps. Other advances include a theory of noncommutative Gleason parts appropriate for D-characters, which uses Harris’ noncommutative hyperbolic metric and Schwarz–Pick inequality, and other ingredients. As an application of Gleason parts we show that in the antisymmetric case, one is guaranteed the existence of a ‘quantum’ Wermer embedding function, and also of non-trivial compact Hankel operators, whenever the Gleason part of the canonical trace is rich in tracial stat
Infant formula for gastro-oesophageal reflux disease
No full textCITATION: Owens, C. J. W., Labuschagne, I. L. & Lombard, M. J. 2012. Infant formula for gastro-oesophageal reflux disease. South African Family Practice, 54(2):106-110.The original publication is available at http://www.safpj.co.zaThickened infant formula is widely used as a first-line treatment for gastro-oesophageal reflux (GOR) in infants. The use thereof remains controversial, and conflicting evidence exists with regards to its efficiency. The safety of anti-reflux formula has been proven, with only a few adverse effects reported, making it safe for infants with mild symptoms of reflux.http://www.safpj.co.za/index.php/safpj/article/view/2337Publisher's versio
Proteomic analysis of proteins responsive to drought and low temperature stress in a hard red spring wheat cultivar
No full textDrought stress is becoming more prevalent with global warming, and has been shown to have large effects on gluten proteins linked to wheat bread making quality. Likewise, low temperature stress can detrimentally affect proteins in wheat. This study was done to determine the differential abundance of high molecular weight (HMW) glutenin proteins in a drought and low temperature stressed high quality hard red spring wheat cultivar (PAN3478), against a control. The treatments were applied in the greenhouse at the soft dough stage. HMW glutenin proteins were extracted from the flour, and were separated by using two-dimensional gel electrophoresis. Protein spots that had p values lower than 0.05 and fold values equal to or greater than 1.2 were considered to be significantly differentially abundant. These proteins were further analyzed by using tandem mass spectrometry. There was a 1.3 to 1.8 fold change in 17 protein spots due to the cold treatment. The drought treatment caused a 1.3 to 3.8 fold change in 19 protein spots. These spots matched either HMW or low molecular weight (LMW) glutenin subunits. In the latter case, the C subunits of LMW glutenins were notably found to be up-regulated under both stress conditions. All the proteins that have been identified can directly influence dough characteristics. Data are available via ProteomeXchange with the identifier PXD017578
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