Search results for " function"

showing 10 items of 9395 documents

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 .

Unit sphereOpen unitApplied Mathematics010102 general mathematicsBanach spaceHolomorphic function01 natural sciences010101 applied mathematicsCombinatoricsBounded functionBall (mathematics)0101 mathematicsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Strongly extreme points and approximation properties

2017

We show that if $x$ is a strongly extreme point of a bounded closed convex subset of a Banach space and the identity has a geometrically and topologically good enough local approximation at $x$, then $x$ is already a denting point. It turns out that such an approximation of the identity exists at any strongly extreme point of the unit ball of a Banach space with the unconditional compact approximation property. We also prove that every Banach space with a Schauder basis can be equivalently renormed to satisfy the sufficient conditions mentioned. In contrast to the above results we also construct a non-symmetric norm on $c_0$ for which all points on the unit sphere are strongly extreme, but …

Unit spherePure mathematicsMathematics::Functional AnalysisApproximation propertyGeneral MathematicsBanach spaceRegular polygonSchauder basisFunctional Analysis (math.FA)Mathematics - Functional Analysis46B20Bounded functionFOS: MathematicsPoint (geometry)Extreme pointMathematics
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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.

Unit spherePure mathematicsMathematics::Functional AnalysisBasis (linear algebra)General Mathematics010102 general mathematicsBanach space01 natural sciencesSchauder basisTask (project management)Functional Analysis (math.FA)Mathematics - Functional Analysis0103 physical sciencesDecomposition (computer science)FOS: Mathematics46B03 46B20 46B26Uncountable set010307 mathematical physics0101 mathematicsMathematics
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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…

Unit spherePure mathematicsMathematics::Functional AnalysisIndex (economics)Existential quantificationOpen problem010102 general mathematicsRegular polygonBanach space01 natural sciencesInfimum and supremumFunctional Analysis (math.FA)Negative - answerMathematics - Functional Analysis0103 physical sciencesFOS: Mathematics46B20 46B22010307 mathematical physics0101 mathematicsAnalysisMathematics
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On holomorphic functions attaining their norms

2004

Abstract We show that on a complex Banach space X , the functions uniformly continuous on the closed unit ball and holomorphic on the open unit ball that attain their norms are dense provided that X has the Radon–Nikodym property. We also show that the same result holds for Banach spaces having a strengthened version of the approximation property but considering just functions which are also weakly uniformly continuous on the unit ball. We prove that there exists a polynomial such that for any fixed positive integer k , it cannot be approximated by norm attaining polynomials with degree less than k . For X=d ∗ (ω,1) , a predual of a Lorentz sequence space, we prove that the product of two p…

Unit spherePure mathematicsMathematics::Functional AnalysisLorentz sequence spaceFunction spaceApproximation propertyApplied MathematicsMathematical analysisBanach spaceHolomorphic functionNorm attainingHolomorphic functionPolynomialUniform continuityNorm (mathematics)Ball (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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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.

Unit sphereSmall diameter46B04 46B20General Mathematics010102 general mathematicsRegular polygon01 natural sciencesMidpointConvexityFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsCombinatoricsNorm (mathematics)FOS: Mathematics0101 mathematicsMathematicsStudia Mathematica
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Rotationally symmetric p -harmonic maps fromD2toS2

2013

We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.

Unit spheresymbols.namesakeClass (set theory)Applied MathematicsDirichlet boundary conditionMathematical analysissymbolsHarmonic mapBoundary (topology)Unit diskAnalysisMathematicsEnergy functionalJournal of Differential Equations
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Le Nazioni Unite

2006

Nel saggio, natura, funzioni e poteri delle Nazioni Unite sono analizzati in una prospettiva storica. In particolare, sono esaminati, per un verso, l''influenza che l''attività dell''Organizzazione (sia normativa che operativa) ha esercitato sullo sviluppo della società internazionale e del suo diritto e, in senso inverso, i condizionamenti degli assetti politici ed economici della società internazionale sul funzionamento dell''Organizzazione. Pertanto, ad una prima parte descrittiva degli organi e delle procedure, seguono due parti, di cui la prima relativa alla vita dell''Organizzazione dalla nascita alla fine della guerra fredda, ed una seconda che parte dalla caduta del muro di Berlino …

United Nations Organizations - Organs of the UN - Functions of the UN - Evolution of the international society.ONU - Organi dell'ONU - Funzioni dell'ONU - Evoluzione della società internazionale.
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Prevention of Functional Decline by Reframing the Role of Nursing Homes?

2017

Institutionalization is generally a consequence of functional decline driven by physical limitations, cognitive impairments, and/or loss of social supports. At this stage, intervention to reverse functional losses is often too late. To be more effective, geriatric medicine must evolve to intervene at an earlier stage of the disability process. Could nursing homes (NHs) transform from settings in which many residents dwell to settings in which the NH residents and those living in neighboring communities benefit from staff expertise to enhance quality of life and maintain or slow functional decline? A task force of clinical researchers met in Toulouse on December 2, 2015, to address some of t…

United StateGerontologymedicine.medical_specialtyActivities of daily livingInstitutionalisationFrail ElderlyCalidad de vidaGerontologíafrailty03 medical and health sciencesMedicina preventiva0302 clinical medicineQuality of life (healthcare)preventionNursingIntervention (counseling)Activities of Daily LivingHumansMedicineCognitive Dysfunction030212 general & internal medicineNursing (all)2901 Nursing (miscellaneous)General NursingHealth policyAgedGeriatricsNursing homebusiness.industryMedicine (all)Health PolicyCognitionGeneral MedicineCognitive reframingUnited StatesNursing Homes3. Good healthGeriatríafunctional declinefrailty; functional decline; Nursing home; prevention; Nursing (all)2901 Nursing (miscellaneous); Medicine (all); Health PolicyGeriatrics and Gerontologybusiness030217 neurology & neurosurgeryHumanJournal of the American Medical Directors Association
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The exact distribution of a weighted Convolution of two Gamma distributions

2006

Si considera una rappresentazione della funzione di densit`a di probabilit`a di una Convoluzione ponderata di distribuzioni Gamma, in cui una funzione ipergeometrica confluente descrive come le differenze tra i parametri di scala delle componenti determinino allontanamenti da una densit`a Gamma. Si considera il caso specifico di una convoluzione di due variabili gamma per mostrare, come al vantaggio interpretativo si aggiunga la possibilit`a di derivare in forma esplicita e computazionalmente semplice, espressioni della funzione di ripartizione e dei momenti. Si mostra la relazione tra tale distribuzione ed il sistema delle distribuzioni di Bessel, e si generalizza inoltre al caso di convol…

Univariate Gamma distribution Bessel function Distribution theory.
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