Search results for "102"
showing 10 items of 2892 documents
Almost square Banach spaces
2014
We single out and study a natural class of Banach spaces -- almost square Banach spaces. In an almost square space we can find, given a finite set $x_1,x_2,\ldots,x_N$ in the unit sphere, a unit vector $y$ such that $\|x_i-y\|$ is almost one. These spaces have duals that are octahedral and finite convex combinations of slices of the unit ball of an almost square space have diameter 2. We provide several examples and characterizations of almost square spaces. We prove that non-reflexive spaces which are M-ideals in their biduals are almost square. We show that every separable space containing a copy of $c_0$ can be renormed to be almost square. A local and a weak version of almost square spa…
Banach spaces where convex combinations of relatively weakly open subsets of the unit ball are relatively weakly open
2018
We introduce and study Banach spaces which have property CWO, i.e., every finite convex combination of relatively weakly open subsets of their unit ball is open in the relative weak topology of the unit ball. Stability results of such spaces are established, and we introduce and discuss a geometric condition---property (co)---on a Banach space. Property (co) essentially says that the operation of taking convex combinations of elements of the unit ball is, in a sense, an open map. We show that if a finite dimensional Banach space $X$ has property (co), then for any scattered locally compact Hausdorff space $K$, the space $C_0(K,X)$ of continuous $X$-valued functions vanishing at infinity has…
Analytic structure in fibers of H∞(Bc0)
2020
Abstract Let H ∞ ( B c 0 ) be the algebra of all bounded holomorphic functions on the open unit ball of c 0 and M ( H ∞ ( B c 0 ) ) the spectrum of H ∞ ( B c 0 ) . We prove that for any point z in the closed unit ball of l ∞ there exists an analytic injection of the open ball B l ∞ into the fiber of z in M ( H ∞ ( B c 0 ) ) , which is an isometry from the Gleason metric of B l ∞ to the Gleason metric of M ( H ∞ ( B c 0 ) ) . We also show that, for some Banach spaces X, B l ∞ can be analytically injected into the fiber M z ( H ∞ ( B X ) ) for every point z ∈ B X .
Polyhedrality and decomposition
2018
Abstract The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable unconditional basis, easier and more transparent. The hypotheses of both results are based on decomposing the unit sphere of a Banach space into countably many pieces, such that each one satisfies certain properties. Some examples of spaces having equivalent polyhedral norms are given.
On Daugavet indices of thickness
2020
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<\delta<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball i…
Boundary blow-up under Sobolev mappings
2014
We prove that for mappings $W^{1,n}(B^n, \R^n),$ continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the unit ball has zero $n$-Hausdorff measure. For H\"older continuous mappings we also prove an essentially sharp generalized Hausdorff dimension estimate.
Diameter 2 properties and convexity
2015
We present an equivalent midpoint locally uniformly rotund (MLUR) renorming $X$ of $C[0,1]$ on which every weakly compact projection $P$ satisfies the equation $\|I-P\| = 1+\|P\|$ ($I$ is the identity operator on $X$). As a consequence we obtain an MLUR space $X$ with the properties D2P, that every non-empty relatively weakly open subset of its unit ball $B_X$ has diameter 2, and the LD2P+, that for every slice of $B_X$ and every norm 1 element $x$ inside the slice there is another element $y$ inside the slice of distance as close to 2 from $x$ as desired. An example of an MLUR space with the D2P, the LD2P+, and with convex combinations of slices of arbitrary small diameter is also given.
Fra selvbergings hushold til forbrukersamfunnet: En matreise gjennom tre generasjoner. En kvalitativ studie av synet på mat, innkjøp av mat og matsvi…
2021
Master´s thesis in Social Science
Distribuciones de probabilidad alternativas para la gestión de riesgo en mercados financieros
2014
Esta tesis se constituye de seis Capítulos y está organizada de la siguiente manera: el primer Capítulo tiene carácter introductorio al tema, se presentan los aspectos preliminares de la investigación, incluyendo los elementos básicos de la teoría financiera. El Capítulo se divide en dos temas: los modelos de valoración de derivados y los cálculos del VaR y CVaR. Adicionalmente en este Capítulo se introducen las familias de distribuciones que se usarán en sus formas estándar con media cero y varianza uno, y se presentan algunas de sus propiedades estadísticas teóricas. Estas familias de distribuciones presentan la ventaja de ser muy flexibles y de ilustrar muchas propiedades de interés en e…
Disentangling human from natural factors: Taphonomical value of microanatomical features on archaeological wood and charcoal assemblages
2020
International audience; Archaeobotanical charcoal and wood analyses rely on the observation of different macro and microanatomical features affecting wood structure to variable extents. These features may result from a wide range of intrinsic and extrinsic factors alluding to different stages of the wood's taphonomical history: initial growth conditions, human selection, transformation/use and discard, post-depositional processes and archaeological sampling strategies. Papers in this volume address taphonomy in this broad sense, through recent methodological work mainly based on experimentation and case studies from a variety of chrono-cultural and geographical contexts. The authors present…